Riemannian Geometry

2. Auflage 2006
ISBN: 978-0-387-29246-5
Verlag: Springer-Verlag New York

Buch, Englisch, Band 171, 405 Seiten, Book, Format (B × H): 155 mm x 235 mm, Gewicht: 1700 g

Reihe: Graduate Texts in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Petersen, Peter

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Riemannian Metrics.- Curvature.- Examples.- Hypersurfaces.- Geodesics and Distance.- Sectional Curvature Comparison I.- The Bochner Technique.- Symmetric Spaces and Holonomy.- Ricci Curvature Comparison.- Convergence.- Sectional Curvature Comparison II.