By José Natário, Leonor Godinho
In contrast to many different texts on differential geometry, this textbook additionally bargains fascinating functions to geometric mechanics and basic relativity.
The first half is a concise and self-contained advent to the fundamentals of manifolds, differential types, metrics and curvature. the second one half reviews functions to mechanics and relativity together with the proofs of the Hawking and Penrose singularity theorems. it may be independently used for one-semester classes in both of those subjects.
The major principles are illustrated and extra constructed through various examples and over three hundred workouts. certain recommendations are supplied for plenty of of those routines, making An advent to Riemannian Geometry excellent for self-study.