Download or read book Hermitian Grassmannian Submanifolds written by Young Jin Suh and published by Springer. This book was released on 2017-09-14 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, which was held at the Kyungpook National University from June 21 to 25, 2016. The Workshop was supported by the Research Institute of Real and Complex Manifolds (RIRCM) and the National Research Foundation of Korea (NRF). The Organizing Committee invited 30 active geometers of differential geometry and related fields from all around the globe to discuss new developments for research in the area. These proceedings provide a detailed overview of recent topics in the field of real and complex submanifolds.
Download or read book Hermitian Grassmannian Submanifolds written by Young Jin Suh and published by . This book was released on 2017 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Geometry and Global Analysis written by Bang-Yen Chen and published by American Mathematical Society. This book was released on 2022-04-07 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930–2017), held January 16, 2020, in Denver, Colorado. Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today. This volume is inspired by his work and his legacy and, while recalling historical results, presents recent developments in the geometry of symmetric spaces as well as generalizations of symmetric spaces; minimal surfaces and minimal submanifolds; totally geodesic submanifolds and their classification; Riemannian, affine, projective, and conformal connections; the $(M_{+}, M_{-})$ method and its applications; and maximal antipodal subsets. Additionally, the volume features recent achievements related to biharmonic and biconservative hypersurfaces in space forms, the geometry of Laplace operator on Riemannian manifolds, and Chen-Ricci inequalities for Riemannian maps, among other topics that could attract the interest of any scholar working in differential geometry and global analysis on manifolds.
Download or read book The Submanifold Geometries Associated to Grassmannian Systems written by Martina Brück and published by American Mathematical Soc.. This book was released on 2002 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
Download or read book Contact Geometry of Slant Submanifolds written by Bang-Yen Chen and published by Springer Nature. This book was released on 2022-06-27 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds. The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ξ┴ -, hemi-slant ξ┴ -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.
Download or read book Real Hypersurfaces in Hermitian Symmetric Spaces written by Jürgen Berndt and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-03-21 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hermitian symmetric spaces are an important class of manifolds that can be studied with methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian symmetric spaces and their submanifolds, and presents classifi cation results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.
Download or read book Complex Geometry of Slant Submanifolds written by Bang-Yen Chen and published by Springer Nature. This book was released on 2022-05-11 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an up-to-date survey and self-contained chapters on complex slant submanifolds and geometry, authored by internationally renowned researchers. The book discusses a wide range of topics, including slant surfaces, slant submersions, nearly Kaehler, locally conformal Kaehler, and quaternion Kaehler manifolds. It provides several classification results of minimal slant surfaces, quasi-minimal slant surfaces, slant surfaces with parallel mean curvature vector, pseudo-umbilical slant surfaces, and biharmonic and quasi biharmonic slant surfaces in Lorentzian complex space forms. Furthermore, this book includes new results on slant submanifolds of para-Hermitian manifolds. This book also includes recent results on slant lightlike submanifolds of indefinite Hermitian manifolds, which are of extensive use in general theory of relativity and potential applications in radiation and electromagnetic fields. Various open problems and conjectures on slant surfaces in complex space forms are also included in the book. It presents detailed information on the most recent advances in the area, making it valuable for scientists, educators and graduate students.
Download or read book Handbook of Differential Geometry Volume 1 written by F.J.E. Dillen and published by Elsevier. This book was released on 1999-12-16 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.
Download or read book Real and Complex Submanifolds written by Young Jin Suh and published by Springer. This book was released on 2014-12-05 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with the Grassmann Research Group, this book contains many important articles delivered at the ICM 2014 Satellite Conference and the 18th International Workshop on Real and Complex Submanifolds, which was held at the National Institute for Mathematical Sciences, Daejeon, Republic of Korea, August 10–12, 2014. The book covers various aspects of differential geometry focused on submanifolds, symmetric spaces, Riemannian and Lorentzian manifolds, and Kähler and Grassmann manifolds.
Download or read book Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds written by Ngaiming Mok and published by World Scientific. This book was released on 1989 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies the problem of characterizing canonical metrics on Hermitian locally symmetric manifolds X of non-compact/compact types in terms of curvature conditions. The proofs of these metric rigidity theorems are applied to the study of holomorphic mappings between manifolds X of the same type. Moreover, a dual version of the generalized Frankel Conjecture on characterizing compact Khler manifolds are also formulated.
Download or read book Minimal Submanifolds and Related Topics written by Y. L. Xin and published by World Scientific. This book was released on 2003 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. This important book presents the Douglas-Rado solution to the Plateau problem, but the main emphasis is on the Bernstein problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and author's own contributions to Bernstein type theorems for higher codimensions. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.
Download or read book Local and Global Methods in Algebraic Geometry written by Nero Budur and published by American Mathematical Soc.. This book was released on 2018-07-26 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12–15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's 60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves.
Download or read book Geometry And Topology Of Submanifolds Iii Proceedings Of The Leeds Differential Geometry Workshop 1990 written by Alan West and published by World Scientific. This book was released on 1991-04-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This workshop collected together works by experts working in various aspects of the differential geometry of submanifold and discussed recent advances and unsolved problems. Two important linking lectures were on the work done by Thorbergsson and others on classifying isoparametric submanifolds of Euclidean spaces and the generalisation of these to Hilbert spaces due to Terng and others. Isoparametric submanifolds provides examples of minimal, taut submanifolds, of harmonic maps and submanifolds with parallel second fundamental form-all topics discussed at this workshop. There were also lectures on the rapidly developing topic of the affine geometry of hypersurfaces and on applications. Amomg the applications discussed are new methods for using PDE's for generating surfaces with special shapes for use in engineering design.
Download or read book Noncommutative Geometry and Physics 2005 written by Ursula Carow-Watamura and published by World Scientific. This book was released on 2007 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space?time in physics. Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field. This self-contained volume contains survey lectures and research articles which address these issues and related topics. The book is accessible to both researchers and graduate students beginning to study this subject.
Download or read book Minimal Submanifolds and Related Topics written by Xin Yuanlong and published by World Scientific. This book was released on 1989-05-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the theory of minimal submanifolds, Bernstein's problem and Plateau's problem are central topics. This important book presents the Douglas-Rado solution to Plateau's problem, but the main emphasis is on Bernstein's problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and the author's own contributions to Bernstein type theorems for higher codimension. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds. This new edition contains the author's recent work on the Lawson-Osserman's problem for higher codimension, and on Chern's problem for minimal hypersurfaces in the sphere. Both Chern's problem and Lawson-Osserman's problem are important problems in minimal surface theory which are still unsolved. In addition, some new techniques were developed to address those problems in detail, which are of interest in the field of geometric analysis.
Download or read book Minimal Surfaces Stratified Multivarifolds and the Plateau Problem written by A. T. Fomenko and published by American Mathematical Soc.. This book was released on 1991-02-21 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plateau's problem is a scientific trend in modern mathematics that unites several different problems connected with the study of minimal surfaces. In its simplest version, Plateau's problem is concerned with finding a surface of least area that spans a given fixed one-dimensional contour in three-dimensional space--perhaps the best-known example of such surfaces is provided by soap films. From the mathematical point of view, such films are described as solutions of a second-order partial differential equation, so their behavior is quite complicated and has still not been thoroughly studied. Soap films, or, more generally, interfaces between physical media in equilibrium, arise in many applied problems in chemistry, physics, and also in nature. In applications, one finds not only two-dimensional but also multidimensional minimal surfaces that span fixed closed ``contours'' in some multidimensional Riemannian space. An exact mathematical statement of the problem of finding a surface of least area or volume requires the formulation of definitions of such fundamental concepts as a surface, its boundary, minimality of a surface, and so on. It turns out that there are several natural definitions of these concepts, which permit the study of minimal surfaces by different, and complementary, methods. In the framework of this comparatively small book it would be almost impossible to cover all aspects of the modern problem of Plateau, to which a vast literature has been devoted. However, this book makes a unique contribution to this literature, for the authors' guiding principle was to present the material with a maximum of clarity and a minimum of formalization. Chapter 1 contains historical background on Plateau's problem, referring to the period preceding the 1930s, and a description of its connections with the natural sciences. This part is intended for a very wide circle of readers and is accessible, for example, to first-year graduate students. The next part of the book, comprising Chapters 2-5, gives a fairly complete survey of various modern trends in Plateau's problem. This section is accessible to second- and third-year students specializing in physics and mathematics. The remaining chapters present a detailed exposition of one of these trends (the homotopic version of Plateau's problem in terms of stratified multivarifolds) and the Plateau problem in homogeneous symplectic spaces. This last part is intended for specialists interested in the modern theory of minimal surfaces and can be used for special courses; a command of the concepts of functional analysis is assumed.
Download or read book Grassmann and Stiefel Varieties over Composition Algebras written by Marek Golasiński and published by Springer Nature. This book was released on 2023-09-17 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with matrix manifolds, i.e., manifolds for which there is a natural representation of their elements as matrix arrays. Classical matrix manifolds (Stiefel, Grassmann and flag manifolds) are studied in a more general setting. It provides tools to investigate matrix varieties over Pythagorean formally real fields. The presentation of the book is reasonably self-contained. It contains a number of nontrivial results on matrix manifolds useful for people working not only in differential geometry and Riemannian geometry but in other areas of mathematics as well. It is also designed to be readable by a graduate student who has taken introductory courses in algebraic and differential geometry.
