**Student Mathematical Library**

Volume: 93;
2020;
243 pp;
Softcover

MSC: Primary 83; 53;

**Print ISBN: 978-1-4704-5628-3
Product Code: STML/93**

List Price: $59.00

Individual Price: $47.20

**Electronic ISBN: 978-1-4704-6313-7
Product Code: STML/93.E**

List Price: $59.00

Individual Price: $47.20

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#### Supplemental Materials

# Curvature of Space and Time, with an Introduction to Geometric Analysis

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*Iva Stavrov*

This book introduces advanced undergraduates
to Riemannian geometry and mathematical general relativity. The
overall strategy of the book is to explain the concept of curvature
via the Jacobi equation which, through discussion of tidal forces,
further helps motivate the Einstein field equations.

After addressing concepts in geometry such as metrics, covariant
differentiation, tensor calculus and curvature, the book explains the
mathematical framework for both special and general
relativity. Relativistic concepts discussed include (initial value
formulation of) the Einstein equations, stress-energy tensor,
Schwarzschild space-time, ADM mass and geodesic incompleteness. The
concluding chapters of the book introduce the reader to geometric
analysis: original results of the author and her undergraduate student
collaborators illustrate how methods of analysis and differential
equations are used in addressing questions from geometry and
relativity. The book is mostly self-contained and the reader is only
expected to have a solid foundation in multivariable and vector
calculus and linear algebra.

The material in this book was first developed for the 2013 summer
program in geometric analysis at the Park City Math Institute, and was
recently modified and expanded to reflect the author's experience of
teaching mathematical general relativity to advanced undergraduates at
Lewis & Clark College.

This book is published in cooperation with IAS/Park City Mathematics Institute

#### Readership

Undergraduate and graduate students interested in differential geometry and relativity.

#### Table of Contents

# Table of Contents

## Curvature of Space and Time, with an Introduction to Geometric Analysis

- Cover Cover11
- Title page iii4
- IAS/Park City Mathematics Institute vii8
- Preface ix10
- Chapter 1. Introduction to Riemannian geometry 114
- Chapter 2. Differential calculus with tensors 4558
- Chapter 3. Curvature 89102
- Chapter 4. General relativity 123136
- Chapter 5. Introduction to geometric analysis 199212
- Bibliography 239252
- Index 241254
- Back Cover Back Cover1259