Riemannian Geometry
A Modern Introduction
(Sprache: Englisch)
This corrected and clarified second edition, first published in 2006, includes a new chapter on the Riemannian geometry of surfaces.
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Produktinformationen zu „Riemannian Geometry “
This corrected and clarified second edition, first published in 2006, includes a new chapter on the Riemannian geometry of surfaces.
Klappentext zu „Riemannian Geometry “
This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.
Inhaltsverzeichnis zu „Riemannian Geometry “
From the Contents:1. Riemannian manifolds; 2. Riemannian curvature; 3. Riemannian volume; 4. Riemannian coverings; 5. Surfaces; 6. Isoperimetric inequalities (constant curvature); 7. The kinetic density; 8. Isoperimetric inequalities (variable curvature); 9. Comparison and finiteness theorems.
Autoren-Porträt von Isaac Chavel
Isaac Chavel is Professor of Mathematics at The City College of the City University of New York. He received his Ph.D. in Mathematics from Yeshiva University under the direction of Professor Harry E. Rauch. He has published in international journals in the areas of differential geometry and partial differential equations, especially the Laplace and heat operators on Riemannian manifolds. His other books include Eigenvalues in Riemannian Geometry (1984) and Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge University Press, 2001). He has been teaching at The City College of the City University of New York since 1970, and has been a member of the doctoral program of the City University of New York since 1976. He is a member of the American Mathematical Society.
Bibliographische Angaben
- Autor: Isaac Chavel
- 2006, 2., überarb. Aufl., 488 Seiten, Maße: 15,2 x 22,9 cm, Kartoniert (TB), Englisch
- Verlag: Cambridge University Press
- ISBN-10: 0521619548
- ISBN-13: 9780521619547
- Erscheinungsdatum: 19.07.2016
Sprache:
Englisch
Rezension zu „Riemannian Geometry “
'... I think that it is the best reference on Riemannian geometry available, especially for someone interested in isoperimetric problems. ... an insightful modern perspective on topics of current research interest.' SIAM Review
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