Download or read book Harmonic Vector Fields on Pseudo Riemannian Manifolds written by Robert Michael Friswell and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Vector Fields written by Sorin Dragomir and published by Elsevier. This book was released on 2011-10-26 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector ?elds with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail. A useful tool for any scientist conducting research in the field of harmonic analysis Provides applications and modern techniques to problem solving A clear and concise exposition of differential geometry of harmonic vector fields on Reimannian manifolds Physical Applications of Geometric Methods
Download or read book Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry written by Ye-lin Ou and published by World Scientific. This book was released on 2020-04-04 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results.Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces.Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics.Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained.This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field.
Download or read book Harmonic Morphisms Between Riemannian Manifolds written by Paul Baird and published by Oxford University Press. This book was released on 2003 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Download or read book The Volume of Vector Fields on Riemannian Manifolds written by Olga Gil-Medrano and published by Springer Nature. This book was released on 2023-07-31 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the study of the volume of vector fields on Riemannian manifolds. Providing a thorough overview of research on vector fields defining minimal submanifolds, and on the existence and characterization of volume minimizers, it includes proofs of the most significant results obtained since the subject’s introduction in 1986. Aiming to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results. The presentation is direct and deviates substantially from the usual approaches found in the literature, requiring a significant revision of definitions, statements, and proofs. A wide range of topics is covered, including: a discussion on the conditions for a vector field on a Riemannian manifold to determine a minimal submanifold within its tangent bundle with the Sasaki metric; numerous examples of minimal vector fields (including those of constant length on punctured spheres); a thorough analysis of Hopf vector fields on odd-dimensional spheres and their quotients; and a description of volume-minimizing vector fields of constant length on spherical space forms of dimension three. Each chapter concludes with an up-to-date survey which offers supplementary information and provides valuable insights into the material, enhancing the reader's understanding of the subject. Requiring a solid understanding of the fundamental concepts of Riemannian geometry, the book will be useful for researchers and PhD students with an interest in geometric analysis.
Download or read book Riemannian Geometry written by Source Wikipedia and published by University-Press.org. This book was released on 2013-09 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 151. Chapters: Nash embedding theorem, Conformal map, Curvature, Geodesic, Riemannian manifold, Riemann curvature tensor, Metric tensor, Holonomy, Symmetric space, De Sitter invariant special relativity, Covariance and contravariance of vectors, Geometrization conjecture, Systolic geometry, Covariant derivative, Hodge dual, Einstein notation, Ricci curvature, Ricci flow, Spin structure, Exponential map, List of formulas in Riemannian geometry, Introduction to systolic geometry, Christoffel symbols, Laplace-Beltrami operator, Glossary of Riemannian and metric geometry, Parallel transport, Gauss-Codazzi equations, Curvature of Riemannian manifolds, Gauss's lemma, Uniformization theorem, Levi-Civita connection, Ricci decomposition, Second fundamental form, Sectional curvature, De Sitter-Schwarzschild metric, Poincare metric, Calibrated geometry, Gravitational instanton, De Sitter space, Calculus of moving surfaces, Hermitian manifold, Tortuosity, Weyl tensor, Scalar curvature, Harmonic map, Cartan-Hadamard theorem, Pseudo-Riemannian manifold, Lie bracket of vector fields, Hermitian symmetric space, Spherical 3-manifold, Geodesics as Hamiltonian flows, Kahler manifold, Abel-Jacobi map, Jacobi field, Constraint counting, Clifford bundle, Killing vector field, Normal coordinates, Systoles of surfaces, Curved space, Fundamental theorem of Riemannian geometry, Theorema Egregium, Hyperkahler manifold, Unit tangent bundle, Sasakian manifold, Loewner's torus inequality, Cartan-Karlhede algorithm, Pu's inequality, Gauss map, Einstein manifold, Recurrent tensor, Soul theorem, Harmonic coordinates, Ruppeiner geometry, Filling radius, G2 manifold, Sub-Riemannian manifold, Quaternion-Kahler manifold, Frobenius manifold, Gromov-Hausdorff convergence, Cheng's eigenvalue comparison theorem, Gromov's systolic inequality for...
Download or read book Introduction to Riemannian Manifolds written by John M. Lee and published by Springer. This book was released on 2019-01-02 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Download or read book Riemannian Manifolds and Homogeneous Geodesics written by Valerii Berestovskii and published by Springer Nature. This book was released on 2020-11-05 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.
Download or read book Harmonic Mappings Between Riemannian Manifolds written by Jürgen Jost and published by . This book was released on 1984 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pseudo Riemannian Geometry delta invariants and Applications written by Bang-yen Chen and published by World Scientific. This book was released on 2011 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold
Download or read book Conformal Vector Fields Ricci Solitons and Related Topics written by Ramesh Sharma and published by Springer Nature. This book was released on 2024-01-19 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data. The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics.
Download or read book Recent Advances in Riemannian and Lorentzian Geometries written by Krishan L. Duggal and published by American Mathematical Soc.. This book was released on 2003 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers material presented by invited speakers at the AMS special session on Riemannian and Lorentzian geometries held at the annual Joint Mathematics Meetings in Baltimore. Topics covered include classification of curvature-related operators, curvature-homogeneous Einstein 4-manifolds, linear stability/instability singularity and hyperbolic operators of spacetimes, spectral geometry of holomorphic manifolds, cut loci of nilpotent Lie groups, conformal geometry of almost Hermitian manifolds, and also submanifolds of complex and contact spaces. This volume can serve as a good reference source and provide indications for further research. It is suitable for graduate students and research mathematicians interested in differential geometry.
Download or read book Infinity harmonic Functions Maps and Morphisms of Riemannian Manifolds written by Tiffany Lynn Troutman and published by . This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Volume of Vector Fields on Riemannian Manifolds written by O. Gil-Medrano and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Regularity for Harmonic Maps and Related Problems written by Roger Moser and published by World Scientific. This book was released on 2005 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a collection of results pertaining to the partial regularity of solutions to various variational problems, all of which are connected to the Dirichlet energy of maps between Riemannian manifolds, and thus related to the harmonic map problem. The topics covered include harmonic maps and generalized harmonic maps; certain perturbed versions of the harmonic map equation; the harmonic map heat flow; and the Landau-Lifshitz (or Landau-Lifshitz-Gilbert) equation. Since the methods in regularity theory of harmonic maps are quite subtle, it is not immediately clear how they can be applied to certain problems that arise in applications. The book discusses in particular this question.
Download or read book Harmonic Maps written by U. R. J. Knill and published by Springer. This book was released on 2006-11-15 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Problems on Conformal Maps of Riemannian and Kaehlerian Manifolds written by S. I. Goldberg and published by . This book was released on 1960 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
