02649nmm a2200277 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002000139245006800159250001700227260004800244300003100292505026800323653002600591653003300617710003400650041001900684989003600703490003400739856007200773082001100845520151500856EB000354594EBX0100000000000000020764600000000000000.0cr|||||||||||||||||||||130626 ||| eng a97803872940321 aPetersen, Peter00aRiemannian GeometryhElektronische Ressourcecby Peter Petersen a2nd ed. 2006 aNew York, NYbSpringer New Yorkc2006, 2006 aXV, 405 pbonline resource0 aRiemannian 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. aDifferential Geometry aGlobal differential geometry2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aGraduate Texts in Mathematics uhttps://doi.org/10.1007/978-0-387-29403-2?nosfx=yxVerlag3Volltext0 a516.36 aIntended 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