An Introduction to Riemannian Geometry

With Applications to Mechanics and Relativity
2014
ISBN: 978-3-319-08665-1
Verlag: Springer-Verlag GmbH

Buch, Englisch, 467 Seiten, Book, Format (B × H): 155 mm x 235 mm, Gewicht: 7197 g

Reihe: Universitext

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Godinho, Leonor

Natário, José

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Differentiable Manifolds.- Differential Forms.- Riemannian Manifolds.- Curvature.- Geometric Mechanics.- Relativity.

Über Autor(innen)

Leonor Godinho is professor at Instituto Superior Técnico (Universidade de Lisboa). She regularly teaches Riemannian geometry, symplectic geometry and introductory geometry courses. Her research activity is focused on symplectic geometry and its connections to algebraic geometry and combinatorics.

José Natário is professor of mathematics at Instituto Superior Técnico (Universidade de Lisboa). He regularly lectures on differential and Riemannian geometry, geometric mechanics and mathematical relativity. His research focuses on general relativity, a subject on which he has published many research papers and a book, “General Relativity Without Calculus” (Springer, 2011).