Prescribing The Curvature Of A Riemannian Manifold
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Author | : Jerry L. Kazdan |
Publisher | : American Mathematical Soc. |
Total Pages | : 68 |
Release | : 1985-12-31 |
Genre | : Mathematics |
ISBN | : 9780821889022 |
Download Prescribing the Curvature of a Riemannian Manifold Book in PDF, Epub and Kindle
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.
Author | : John M. Lee |
Publisher | : Springer Science & Business Media |
Total Pages | : 232 |
Release | : 2006-04-06 |
Genre | : Mathematics |
ISBN | : 0387227261 |
Download Riemannian Manifolds Book in PDF, Epub and Kindle
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.
Author | : John M. Lee |
Publisher | : Springer |
Total Pages | : 437 |
Release | : 2019-01-02 |
Genre | : Mathematics |
ISBN | : 3319917552 |
Download Introduction to Riemannian Manifolds Book in PDF, Epub and Kindle
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.
Author | : Vladimir Rovenski |
Publisher | : Springer Science & Business Media |
Total Pages | : 296 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461242703 |
Download Foliations on Riemannian Manifolds and Submanifolds Book in PDF, Epub and Kindle
This monograph is based on the author's results on the Riemannian ge ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature. The main idea is that such foliated (sub) manifolds can be decom posed when the dimension of the leaves (generators) is large. The methods of investigation are mostly synthetic. The work is divided into two parts, consisting of seven chapters and three appendices. Appendix A was written jointly with V. Toponogov. Part 1 is devoted to the Riemannian geometry of foliations. In the first few sections of Chapter I we give a survey of the basic results on foliated smooth manifolds (Sections 1.1-1.3), and finish in Section 1.4 with a discussion of the key problem of this work: the role of Riemannian curvature in the study of foliations on manifolds and submanifolds.
Author | : Katsuhiro Shiohama |
Publisher | : Springer |
Total Pages | : 343 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540388273 |
Download Curvature and Topology of Riemannian Manifolds Book in PDF, Epub and Kindle
Author | : Bang-yen Chen |
Publisher | : World Scientific |
Total Pages | : 510 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9814329649 |
Download Pseudo-Riemannian Geometry, [delta]-invariants and Applications Book in PDF, Epub and Kindle
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
Author | : Ulrich Dierkes |
Publisher | : |
Total Pages | : 17 |
Release | : 1986 |
Genre | : |
ISBN | : |
Download A geometric maximum principle for surfaces of prescribed mean curvature in Riemannian manifolds Book in PDF, Epub and Kindle
Author | : Daniel W. Stroock |
Publisher | : American Mathematical Soc. |
Total Pages | : 290 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821838393 |
Download An Introduction to the Analysis of Paths on a Riemannian Manifold Book in PDF, Epub and Kindle
Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.
Author | : Steven Rosenberg |
Publisher | : Cambridge University Press |
Total Pages | : 190 |
Release | : 1997-01-09 |
Genre | : Mathematics |
ISBN | : 9780521468312 |
Download The Laplacian on a Riemannian Manifold Book in PDF, Epub and Kindle
This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Author | : Junjie Tang |
Publisher | : |
Total Pages | : 94 |
Release | : 1992 |
Genre | : Curvature |
ISBN | : |
Download Prescribing Curvature on Manifolds with Singularities Book in PDF, Epub and Kindle