Overview
This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (the Koszul formula in disguise); an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus integrated into the text, allowing for an early treatment of the Sphere theorem using a forgotten proof by Berger; recent results regarding manifolds with positive curvature.
Full Product Details
Author: Peter Petersen
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: 2nd ed. 2006
Volume: v. 171
Dimensions:
Width: 15.60cm
, Height: 2.30cm
, Length: 23.40cm
Weight: 0.769kg
ISBN: 9780387292465
ISBN 10: 0387292462
Pages: 420
Publication Date: 01 August 2006
Audience:
College/higher education
,
Undergraduate
Replaced By: 9783319266527
Format: Hardback
Publisher's Status: Out of Print
Availability: In Print
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.
Reviews
From the reviews of the second edition:P. Petersen Riemannian Geometry ""A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics."" -EUROPEAN MATHEMATICAL SOCIETY ""This is an introduction to modern methods in Riemannian geometry containing interesting and original approaches to many areas in this field. ... After a general introduction (metrics, curvature, geodesics) and concrete calculations for many examples, the second half of the book considers Bochner-Cartan techniques and comparison geometry. Particularly for these aspects it continues to play an outstanding role among textbooks in Riemannian geometry."" (M. Kunzinger, Monatshefte fur Mathematik, Vol. 154 (1), May, 2008)
From the reviews of the second edition:P. Petersen Riemannian Geometry A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics. -EUROPEAN MATHEMATICAL SOCIETY This is an introduction to modern methods in Riemannian geometry containing interesting and original approaches to many areas in this field. ... After a general introduction (metrics, curvature, geodesics) and concrete calculations for many examples, the second half of the book considers Bochner-Cartan techniques and comparison geometry. Particularly for these aspects it continues to play an outstanding role among textbooks in Riemannian geometry. (M. Kunzinger, Monatshefte fur Mathematik, Vol. 154 (1), May, 2008)
P. Petersen <p>Riemannian Geometry <p> A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics. <p>a EUROPEAN MATHEMATICAL SOCIETY
