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© 2014

An Introduction to Riemannian Geometry

With Applications to Mechanics and Relativity

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-x
  2. Leonor Godinho, José Natário
    Pages 1-59
  3. Leonor Godinho, José Natário
    Pages 61-94
  4. Leonor Godinho, José Natário
    Pages 95-122
  5. Leonor Godinho, José Natário
    Pages 123-164
  6. Leonor Godinho, José Natário
    Pages 165-250
  7. Leonor Godinho, José Natário
    Pages 251-319
  8. Leonor Godinho, José Natário
    Pages 321-454
  9. Back Matter
    Pages 455-467

About this book

Introduction

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.

Keywords

General Relativity Geometric Mechanics Riemannian Geometry Singularity Theorems

Authors and affiliations

  1. 1.Departamento de MatemáticaInstituto Superior TécnicoLisbonPortugal
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisbonPortugal

About the authors

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).

Bibliographic information

Reviews

From the book reviews:

“The aim of the textbook is twofold. First, it is a concise and self-contained quick introduction to the basics of differential geometry, including differential forms, followed by the main ideas of Riemannian geometry. Second, the last two chapters are devoted to some interesting applications to geometric mechanics and relativity. … the book is well written and also very readable. I warmly recommend it to specialists in mathematics, physics and engineering, especially to Ph.D. students.” (Miroslaw Doupovec, zbMATH 1306.53001, 2015)