Tag: Curvature

Free Download G. S. Hall, "SYMMETRIES AND CURVATURE STRUCTURE IN GENERAL RELATIVITY "
English | ISBN: 9810210515 | 2004 | 440 pages | PDF | 20 MB
Hall (U. of Aberdeen) compiles the theoretical aspects of the literature on symmetries in general relativity that have been produced over the past few decades. He is not offering a textbook, he warns, but a study of certain aspects of four-dimensional Lorentzian differential geometry emphasizing the special requirements of Einstein’s general theory of relativity. His main goal is to present a mathematical approach to symmetries and to the related topic of the connection and curvature structure of space-time, without paying much attention to attendant problems that worry mathematicians more than physicists. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

Free Download Exploring Curvature By Professor James Casey (auth.)
1996 | 291 Pages | ISBN: 3528064757 | PDF | 19 MB
This introductory book, which is intuitive and exploratory in nature, is intended as a bridge between Euclid’s geometry and the modern geometry of curved spaces. It is organized around a collection of simple experiments which the reader can perform at home or in a classroom setting. Methods for physically exploring the intrinsic geometry of commonplace curved objects (such as bowls, balls and watermelons) are described. The concepts of Gaussian curvature, parallel transport, and geodesics are treated. The book also contains biographical chapters on Gauss, Riemann, and Levi- Civita.

Free Download Manifolds of Nonpositive Curvature by Werner Ballmann , Mikhael Gromov , Viktor Schroeder
English | PDF | 1985 | 280 Pages | ISBN : 146849161X | 13.5 MB
This volume presents a complete and self-contained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the Collège de France in Paris. Among others these lectures threat local and global rigidity problems (e.g., a generalization of the famous Mostow rigidity theorem) and finiteness results for manifolds of finite volume. V. Schroeder wrote up these lectures, including complete and detailed proofs. A lot of background material is added to the first lectures. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank.

Free Download Klaus Ecker, "Regularity Theory for Mean Curvature Flow"
English | 2004 | pages: 192 | ISBN: 0817637818, 0817632433 | PDF | 2,8 mb
Mean curvature flow and related flows are important tools in mathematics and mathematical physics. For example, the famous Penrose conjecture in general relativity by Huisken and Ilmanan was based on a curvature flow approach. Under mean curvature flow, surfaces usually develop singularities in finite time. This book presents techniques in the study of singularities of mean curvature flow. It details the influential work of K. Brakke as well as such recent developments as relations to regularity theory for minimal surfaces, as in Allard’s and de Giorgi’s work.