Riemannian Geometry and Geometric Analysis (Universitext) - Softcover

Jost, Jurgen

Softcover

ISBN 10: 3540571132 ISBN 13: 9783540571131

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1995

Synopsis

This textbook introduces techniques from nonlinear analysis at an early stage. Such techniques have recently become an indispensable tool in research in geometry, and they are treated here for the first time in a textbook. Topics include: Differentiable and Riemannian manifolds, metric properties, tensor calculus, vector bundles; the Hodge Theorem for de Rham cohomology; connections and curvature, the Yang-Mills functional; geodesics and Jacobi fields, Rauch comparison theorem and applications; Morse theory (including an introduction to algebraic topology), applications to the existence of closed geodesics; symmetric spaces and Kahler manifolds; the Palais-Smale condition and closed geodesics; Harmonic maps, minimal surfaces.

About this title

Review

From the reviews of the sixth edition:

“For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained ... . The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field. This sixth edition contains a deeper study of the spectrum of the Laplace operator and its relation to the geometry of the underlying Riemannian manifold.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 171 (3-4), September, 2013)

“The present book is the sixth edition of the author’s textbook on Riemannian geometry and geometric analysis. In general, it gives a synthesis of geometric and analytic methods in the study of Riemannian manifolds. ... the book is well written. That is why I would recommend it to specialists in mathematics or physics and especially to Ph.D. students of differential geometry.” (Miroslaw Doupovec, Zentralblatt MATH, Vol. 1227, 2012)

From the Back Cover

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research.This new edition introduces and explains the ideas of the parabolic methods that have recently found such a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. [..] The book is made more interesting by the perspectives in various sections." Mathematical Reviews

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1995
• Language: English
• ISBN 10: 3540571132
• ISBN 13: 9783540571131
• Binding: Paperback
• Edition number: 2
• Number of pages: 412