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Informationen zum Autor 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. Klappentext This corrected and clarified second edition! including a new chapter on the Riemannian geometry of surfaces! provides an introduction to the geometry of curved spaces. Its main themes are the effect of the curvature of these spaces on the usual notions of classical Euclidean geometry and the new notions and ideas motivated by curvature itself. An ambitious Notes and Exercises section is included with each chapter. The book! which could be used as the basis for a graduate course! will appeal to graduate students and researchers in differential geometry and topology! analysis and differential equations. Zusammenfassung This corrected and clarified second edition! first published in 2006! includes a new chapter on the Riemannian geometry of surfaces and provides an introduction to the geometry of curved spaces. Its main theme is the effect of the curvature of spaces on the usual notions of geometry! angles! lengths! areas! and volumes! and on those new notions and ideas motivated by curvature itself. Inhaltsverzeichnis 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....
