Download or read book Almost Complex Homogeneous Spaces and Their Submanifolds written by Kichoon Yang and published by World Scientific. This book was released on 1987 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of almost complex homogeneous spaces and certain closely related class of spaces, so called partial G-flag manifolds. Submanifolds, in particular holomorphic curves, are also treated using the theory of moving frames and the structure theory of compact lie groups. The exposition is reasonably self-contained and this book is strongly recommended as a text for beginning graduate students.
Download or read book Harmonic Maps Into Homogeneous Spaces written by Malcolm Black and published by Routledge. This book was released on 2018-05-04 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been made in understanding harmonic maps of Riemann surfaces into symmetric spaces. In particular, ""twistor methods"" construct some, and in certain cases all, such mappings from holomorphic data. These notes develop techniques applicable to more general homogeneous manifolds, in particular a very general twistor result is proved. When applied to flag manifolds, this wider viewpoint allows many of the previously unrelated twistor results for symmetric spaces to be brought into a unified framework. These methods also enable a classification of harmonic maps into full flag manifolds to be established, and new examples are constructed. The techniques used are mostly a blend of the theory of compact Lie groups and complex differential geometry. This book should be of interest to mathematicians with experience in differential geometry and to theoretical physicists.
Download or read book Nonselfadjoint Operator Algebras Operator Theory and Related Topics written by H. Bercovicii and published by Birkhäuser. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Carl Pearcy on the occasion of his 60th birthday, presents recent results in operator theory, nonselfadjoint operator algebras, measure theory and the theory of moments. The articles on these subjects have been contributed by leading area experts, many of whom were associated with Carl Pearcy as students or collaborators. The book testifies to his multifaceted interests and includes a biographical sketch and a list of publications.
Download or read book Geometry of Submanifolds and Homogeneous Spaces written by Andreas Arvanitoyeorgos and published by MDPI. This book was released on 2020-01-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered.
Download or read book Complete Minimal Surfaces of Finite Total Curvature written by Kichoon Yang and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is based upon the philosophy that the study of finite total curvature complete minimal surfaces in R3, in large measure, coincides with the study of meromorphic functions and linear series on compact Riemann sur faces. This philosophy is first indicated in the fundamental theorem of Chern and Osserman: A complete minimal surface M immersed in R3 is of finite total curvature if and only if M with its induced conformal structure is conformally equivalent to a compact Riemann surface Mg punctured at a finite set E of points and the tangential Gauss map extends to a holomorphic map Mg _ P2. Thus a finite total curvature complete minimal surface in R3 gives rise to a plane algebraic curve. Let Mg denote a fixed but otherwise arbitrary compact Riemann surface of genus g. A positive integer r is called a puncture number for Mg if Mg can be conformally immersed into R3 as a complete finite total curvature minimal surface with exactly r punctures; the set of all puncture numbers for Mg is denoted by P (M ). For example, Jorge and Meeks [JM] showed, by constructing an example g for each r, that every positive integer r is a puncture number for the Riemann surface pl.
Download or read book Two Algebraic Byways from Differential Equations Gr bner Bases and Quivers written by Kenji Iohara and published by Springer Nature. This book was released on 2020-02-20 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.
Download or read book Compact Riemann Surfaces And Algebraic Curves written by Kichoon Yang and published by World Scientific. This book was released on 1988-11-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an introduction to the theory of Compact Riemann Surfaces and algebraic curves. It gives a concise account of the elementary aspects of different viewpoints in curve theory. Foundational results on divisors and compact Riemann surfaces are also stated and proved.
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 Prospects Of Differential Geometry And Its Related Fields Proceedings Of The 3rd International Colloquium On Differential Geometry And Its Related Fields written by Toshiaki Adachi and published by World Scientific. This book was released on 2013-09-24 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of contributions by the main participants of the 3rd International Colloquium on Differential Geometry and its Related Fields (ICDG2012), which was held in Veliko Tarnovo, Bulgaria. Readers will find original papers by specialists and well-organized reports of recent developments in the fields of differential geometry, complex analysis, information geometry, mathematical physics and coding theory. This volume provides significant information that will be useful to researchers and serves as a good guide for young scientists. It is also for those who wish to start investigating these topics and interested in their interdisciplinary areas.
Download or read book New Horizons In Differential Geometry And Its Related Fields written by Toshiaki Adachi and published by World Scientific. This book was released on 2022-04-07 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.
Download or read book Foundations of Differential Geometry Volume 2 written by Shoshichi Kobayashi and published by John Wiley & Sons. This book was released on 1996-02-22 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1969 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis and Algebra on Differentiable Manifolds A Workbook for Students and Teachers written by P.M. Gadea and published by Springer Science & Business Media. This book was released on 2009-12-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: A famous Swiss professor gave a student’s course in Basel on Riemann surfaces. After a couple of lectures, a student asked him, “Professor, you have as yet not given an exact de nition of a Riemann surface.” The professor answered, “With Riemann surfaces, the main thing is to UNDERSTAND them, not to de ne them.” The student’s objection was reasonable. From a formal viewpoint, it is of course necessary to start as soon as possible with strict de nitions, but the professor’s - swer also has a substantial background. The pure de nition of a Riemann surface— as a complex 1-dimensional complex analytic manifold—contributes little to a true understanding. It takes a long time to really be familiar with what a Riemann s- face is. This example is typical for the objects of global analysis—manifolds with str- tures. There are complex concrete de nitions but these do not automatically explain what they really are, what we can do with them, which operations they really admit, how rigid they are. Hence, there arises the natural question—how to attain a deeper understanding? One well-known way to gain an understanding is through underpinning the d- nitions, theorems and constructions with hierarchies of examples, counterexamples and exercises. Their choice, construction and logical order is for any teacher in global analysis an interesting, important and fun creating task.
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 2022-04-04 with total page 388 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 classification 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 New Zealand Journal of Mathematics written by and published by . This book was released on 1996 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Progress in Differential Geometry and Its Related Fields written by Toshiaki Adachi and published by World Scientific. This book was released on 2012 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions by the main participants of the 2nd International Colloquium on Differential Geometry and its Related Fields (ICDG2010), held in Veliko Tarnovo, Bulgaria to exchange information on current topics in differential geometry, information geometry and applications. These contributions from active specialists in differential geometry provide significant information on research papers which cover geometric structures, concrete Lie group theory and information geometry. This volume is invaluable not only for researchers in this special area but also for those who are interested in interdisciplinary areas in differential geometry, complex analysis, probability theory and mathematical physics. It also serves as a good guide to graduate students in the field of differential geometry.
