This 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.
What people are saying - Write a review
Other editions - View all
Riemannian geometry - Wikipedia, the free encyclopedia
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, ie with an inner ...
en.wikipedia.org/ wiki/ Riemannian_geometry
Home page for 765
Math 765 Riemannian Geometry (Spring 2007) ... Riemannian Geometry by Peter Petersen. Differential Geometry Volume I by Spivak. Riemannian Geometry by Do ...
www.math.wisc.edu/ ~jeffv/ courses/ 765_S07.html
Zentralblatt MATH Database 1931 – 2008 0914.53001
This monograph is an advanced introduction to Riemannian geometry – advanced, be-. cause a lot of material appearing in other books on Riemannian geometry ...
zmath.impa.br/ cgi-bin/ zmen/ ZMATH/ en/ quick.html?first=1&
Mathematics 217B: Differential Geometry
"Comparison Theorems in Riemannian Geometry" by Jeff Cheeger and David Ebin (excellent text, ... "Riemannian Geometry and Geometric Analysis" by Jurgen Jost ...
math.stanford.edu/ ~brendle/ math217b.html
Differential Geometry (250) graduate course, Fall 2005
This is a good mathematical treatment of Riemannian geometry and general ... They don't go very much into Riemannian geometry, but are very good on ...
math.ucsd.edu/ ~justin/ 250.html
An Introduction to Riemannian Geometry
purpose is to introduce the beautiful theory of Riemannian Geometry ... The study of Riemannian geometry is rather meaningless without ...
www.maths.lth.se/ matematiklu/ personal/ sigma/ Riemann.pdf
Syllabus of the Oral Test
Riemannian Geometry. Manifolds, Differential Structure ... Karsten Grove, Riemannian Geometry: A Metric Entrance. Peter Petersen, Riemannian Geometry ...
www.math.rutgers.edu/ f07/ grad/ phd_requirements/ oral/ li.ps
Citebase - Ricci Flow and the Poincare Conjecture
Comparison theorems in Riemannian geometry. North-Holland Publishing Co., .... Riemannian geometry, Second Edition, volume 171 of Graduate Texts in ...
Mathematics of Computation
Marcel Berger, Riemannian geometry during the second half of the twentieth century, University Lecture Series, Volume 17, AMS, Providence RI (2000). ...
www.ams.org/ mcom/ 2006-75-256/ S0025-5718-06-01924-7/ home.html
Colloquium Seminar Abstracts
(September 7) Professor Peter Petersen: Distance Estimates in Riemannian Geometry - The talk will be a survey of old and recent work on results about ...
www.math.umd.edu/ research/ seminars/ colloquium/ abstracts01-02.html