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LEADER: 03058nam a22004095a 4500
001 013841482-3
005 20131206202340.0
008 130426s1998 xxu| s ||0| 0|eng d
020 $a9781475764345
020 $a9781475764345
020 $a9781475764369
024 7 $a10.1007/978-1-4757-6434-5$2doi
035 $a(Springer)9781475764345
040 $aSpringer
050 4 $aQA641-670
072 7 $aPBMP$2bicssc
072 7 $aMAT012030$2bisacsh
082 04 $a516.36$223
100 1 $aPetersen, Peter,$eauthor.
245 10 $aRiemannian Geometry /$cby Peter Petersen.
264 1 $aNew York, NY :$bSpringer New York :$bImprint: Springer,$c1998.
300 $aXVI, 434 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v171
505 0 $aContents: Introduction -- Riemannian Metrics -- Curvature -- Examples -- Hypersurfaces -- Geodesics and Distance -- Sectional Curvature Comparison I -- The Bochner Technique -- Symmetric Spaces and Holony -- Ricci Curvature Comparison -- Convergence -- Sectional Curvature Comparison II -- Appendices. A: DeRham Cohomology. B: Principal Bundles. C: Spinors -- Bibliography.
520 $aThis book is intended for a one year course in Riemannian Geometry. It will serve 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. Instead of variational techniques, the author uses a unique approach emphasizing distance functions and special coordinate systems. He also uses standard calculus with some techniques from differential equations, instead of variational calculus, thereby providing a more elementary route for students. Many of the chapters contain material typically found in specialized texts and never before published together in one source. Key sections include noteworthy coverage of: geodesic geometry, Bochner technique, symmetric spaces, holonomy, comparison theory for both Ricci and sectional curvature, and convergence theory. This volume is one of the few published works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory as well as presenting the most up-to-date research including sections on convergence and compactness of families of manifolds. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stoke's theorem. Scattered throughout the text is a variety of exercises which will help to motivate readers to deepen their understanding of the subject.
650 20 $aGeometry, Differential.
650 10 $aMathematics.
650 0 $aMathematics.
650 0 $aGlobal differential geometry.
776 08 $iPrinted edition:$z9781475764369
830 0 $aGraduate Texts in Mathematics ;$v171.
988 $a20131119
906 $0VEN