Riemannian Geometry 1st 1992. Corr edition by do Carmo, Manfredo P. (2013) Hardcover

by Manfredo P. Do Carmo

This text has been adopted University of Pennsylvania, Philadelphia University of Connecticut, Storrs Duke University, Durham, NC California Institute of Technology, Pasadena University of Washington, Seattle Swarthmore College, Swarthmore, PA University of Chicago, IL University of Michigan, Ann Arbor "In the reviewer's opinion, this is a superb book which makes learning a real pleasure." ¿ Revue Romaine de Mathematiques Pures et Appliquees "This main-stream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises." ¿ Monatshefte F. Mathematik "This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry." ¿ Publicationes Mathematicae Differential Manifolds * Riemannian Metrics * Affine Connections; Riemannian Connections * Geodesics; Convex Neighborhoods * Curvature * Jacobi Fields * Isometric Immersions * Complete Manifolds; Hopf-Rinow and Hadamard Theorems * Spaces of Constant Curvature * Variations of Energy * The Rauch Comparison Theorem * The Morse Index Theorem * The Fundamental Group of Manifolds of Negative Curvature * The Sphere Theorem * Index Theory and Applications

Genres: Mathematics, Geometry, Science, Textbooks, Reference

Hardcover

First published January 1, 2008

About the author

Manfredo Perdigão do Carmo (15 August 1928, Maceió – 30 April 2018, Rio de Janeiro) was a Brazilian mathematician. He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil.

Reviews

[Bogdan Suceava · Rating 5 out of 5]

The best introduction in the fundamental topics of Riemannian Geometry. This book helped me a lot. M. P. do Carmo accomplished a very useful construction that most probably will help several generations of mathematicians as they advance in this topic.

[Wissam Raji · Rating 5 out of 5]

I would say one of the best introductory books to Riemannian geometry with a nice simplification of treatment of the fundamental topics.

[Ella Novella · Rating 2 out of 5]

The cover image goes hard af and I want a tattoo of it. But oh my god was this a hard read starting from 0 knowledge of manifolds. Lesson learned: Start by learning the topology before tacking on a metric.