Total Curvature In Riemannian Geometry
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Total Curvature In Riemannian Geometry
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Author : Thomas Willmore
language : en
Publisher:
Release Date : 1982
Total Curvature In Riemannian Geometry written by Thomas Willmore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
Total Curvature In Riemannian Geometry
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Author : Thomas Willmore
language : en
Publisher: Halsted Press
Release Date : 1982
Total Curvature In Riemannian Geometry written by Thomas Willmore and has been published by Halsted Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Courbure categories.
Riemannian Manifolds
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Author : John M. Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
Riemannian Manifolds written by John M. Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.
This book is designed as a textbook for a one-quarter or one-semester graduate course on Riemannian geometry, for students who are familiar with topological and differentiable manifolds. It focuses on developing an intimate acquaintance with the geometric meaning of curvature. In so doing, it introduces and demonstrates the uses of all the main technical tools needed for a careful study of Riemannian manifolds. The author has selected a set of topics that can reasonably be covered in ten to fifteen weeks, instead of making any attempt to provide an encyclopedic treatment of the subject. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics,without which one cannot claim to be doing Riemannian geometry. It then introduces the Riemann curvature tensor, and quickly moves on to submanifold theory in order to give the curvature tensor a concrete quantitative interpretation. From then on, all efforts are bent toward proving the four most fundamental theorems relating curvature and topology: the Gauss–Bonnet theorem (expressing the total curvature of a surface in term so fits topological type), the Cartan–Hadamard theorem (restricting the topology of manifolds of nonpositive curvature), Bonnet’s theorem (giving analogous restrictions on manifolds of strictly positive curvature), and a special case of the Cartan–Ambrose–Hicks theorem (characterizing manifolds of constant curvature). Many other results and techniques might reasonably claim a place in an introductory Riemannian geometry course, but could not be included due to time constraints.
The Geometry Of Total Curvature On Complete Open Surfaces
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Author : Katsuhiro Shiohama
language : en
Publisher: Cambridge University Press
Release Date : 2003-11-13
The Geometry Of Total Curvature On Complete Open Surfaces written by Katsuhiro Shiohama and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-13 with Mathematics categories.
This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.
The Ricci Flow In Riemannian Geometry
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Author : Ben Andrews
language : en
Publisher: Springer Science & Business Media
Release Date : 2011
The Ricci Flow In Riemannian Geometry written by Ben Andrews and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
Riemannian Geometry In An Orthogonal Frame
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Author : Elie Cartan
language : en
Publisher: World Scientific
Release Date : 2001
Riemannian Geometry In An Orthogonal Frame written by Elie Cartan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Elie Cartan's book Geometry of Riemannian Manifolds (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951, and 3rd printing, 1988). Cartan's lectures in 1926-27 were different -- he introduced exterior forms at the very beginning and used extensively orthonormal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book Riemannian Geometry in an Orthogonal Frame (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fiber bundle of a submanifold, etc. The only book of Elie Cartan that was not available in English, it has now been translated into English by Vladislav V Goldberg, the editor of the Russian edition.
Handbook Of Differential Geometry Volume 1
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Author : F.J.E. Dillen
language : en
Publisher: Elsevier
Release Date : 1999-12-16
Handbook Of Differential Geometry Volume 1 written by F.J.E. Dillen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-16 with Mathematics categories.
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.
Curvature And Topology Of Riemannian Manifolds
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Author : Katsuhiro Shiohama
language : en
Publisher: Springer
Release Date : 2006-11-14
Curvature And Topology Of Riemannian Manifolds written by Katsuhiro Shiohama and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Riemannian Geometry
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Author : Isaac Chavel
language : en
Publisher: Cambridge University Press
Release Date : 1995-01-27
Riemannian Geometry written by Isaac Chavel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-27 with Mathematics categories.
This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject.
Prescribing The Curvature Of A Riemannian Manifold
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Author : Jerry L. Kazdan
language : en
Publisher: American Mathematical Soc.
Release Date : 1985-12-31
Prescribing The Curvature Of A Riemannian Manifold written by Jerry L. Kazdan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-12-31 with Mathematics categories.
These notes were the basis for a series of ten lectures given in January 1984 at Polytechnic Institute of New York under the sponsorship of the Conference Board of the Mathematical Sciences and the National Science Foundation. The lectures were aimed at mathematicians who knew either some differential geometry or partial differential equations, although others could understand the lectures. Author's Summary:Given a Riemannian Manifold $(M,g)$ one can compute the sectional, Ricci, and scalar curvatures. In other special circumstances one also has mean curvatures, holomorphic curvatures, etc. The inverse problem is, given a candidate for some curvature, to determine if there is some metric $g$ with that as its curvature. One may also restrict ones attention to a special class of metrics, such as Kahler or conformal metrics, or those coming from an embedding. These problems lead one to (try to) solve nonlinear partial differential equations. However, there may be topological or analytic obstructions to solving these equations. A discussion of these problems thus requires a balanced understanding between various existence and non-existence results. The intent of this volume is to give an up-to-date survey of these questions, including enough background, so that the current research literature is accessible to mathematicians who are not necessarily experts in PDE or differential geometry. The intended audience is mathematicians and graduate students who know either PDE or differential geometry at roughly the level of an intermediate graduate course.