EAN: 9783319086651

UNIVERSITEXT AN INTRODUCTION TO RIEMANNIAN GE...

Unlike many other texts on differential geometry  this textbook also offers interesting
applications to geometric mechanics and general relativity. The first part is a concise and
self-contained introduction to the basics of manifolds  differential forms  metrics and
curvature. The second part studies applications to mechanics and relativity including the
proofs of the Hawking and Penrose singularity theorems. It can be independently used for
one-semester courses in either of these subjects. The main ideas are illustrated and further
developed by numerous examples and over 300 exercises. Detailed solutions are provided for many
of these exercises  making An Introduction to Riemannian Geometry ideal for self-study.

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