Riemannian Geometry by Peter Petersen
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.
From the reviews of the second edition: PPetersen 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)
Peter Petersen is a Professor of Mathematics at UCLA. His current research is on various aspects of Riemannian geometry. Professor Petersen has authored two important textbooks for Springer: Riemannian Geometry in the GTM series and Linear Algebra in the UTM series.
| SKU | Unavailable |
| ISBN 13 | 9780387292465 |
| ISBN 10 | 0387292462 |
| Title | Riemannian Geometry |
| Author | Peter Petersen |
| Series | Graduate Texts In Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Springer-Verlag New York Inc. |
| Year published | 2006-08-01 |
| Number of pages | 420 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |