03208nam a22004335i 4500 978-0-387-29403-2 DE-He213 20260521091853.0 cr nn 008mamaa 100301s2006 xxu| s |||| 0|eng d 9780387294032 99780387294032 10.1007/978-0-387-29403-2 doi CICY 516.36 23 Petersen, Peter. author. Riemannian Geometry [recurso electrónico] / by Peter Petersen. Second Edition. New York, NY : Springer New York, 2006. XVI, 408 p. 59 illus. online resource. text txt rdacontent computer c rdamedia recurso en línea cr rdacarrier text file PDF rda Graduate Texts in Mathematics, 0072-5285 ; 171 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. Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject. Important additions to this new edition include: * A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise; * An increased number of coordinate calculations of connection and curvature; * General fomulas for curvature on Lie Groups and submersions; * Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger; * Several recent results about manifolds with positive curvature. From reviews of the first edition: "The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type." - Bernd Wegner, Zentralblatt MATHEMATICS. GLOBAL DIFFERENTIAL GEOMETRY. MATHEMATICS. DIFFERENTIAL GEOMETRY. SpringerLink (Online service) Springer eBooks Printed edition: 9780387292465 Graduate Texts in Mathematics, 0072-5285 ; 171 http://dx.doi.org/10.1007/978-0-387-29403-2 Ver el texto completo en las instalaciones del CICY ddc ER 32892 32892 0 0 ddc 0 0 LE CICY CICY EL 2025-07-10 0 516.36 2025-07-10 08:39:44 2025-07-10 ER