Riemannian Geometry

Graduate Texts in Mathematics #171

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.

Genres: Mathematics, Geometry, Science

405 pages, Hardcover

First published November 7, 1997

Reviews

[Colin Hinde · Rating 5 out of 5]

Will anyone on this website read this book based on my recommendation?

[Filip Dul · Rating 4 out of 5]

There are so many fantastic geometric expressions described in this book. The writing can be a bit dry—I wish the author would provide more intuition about certain facts—but this compendium should be on every differential geometer’s shelf.