Riemannian Geometry / Edition 1

Riemannian Geometry / Edition 1

Pub. Date:
Birkhauser Verlag

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Riemannian Geometry / Edition 1

Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese)for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text.

A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to bea significant contribution to this highly applicable and stimulating subject.

Product Details

ISBN-13: 9780817634902
Publisher: Birkhauser Verlag
Publication date: 01/01/1992
Series: Mathematics: Theory & Applications Series
Edition description: 1st ed. 1992, Corr. 14th printing 2013
Pages: 300
Product dimensions: 6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

Preface to the 1st edition
• Preface to the 2nd edition
• Preface to the English edition
• How to use this book
• 0. Differentiable Manifolds
• 1. Riemannian Metrics
• 2. Affine Connections; Riemannian Connections
• 3. Geodesics; Convex Neighborhoods
• 4. Curvature
• 5. Jacobi Fields
• 6. Isometric Immersions
• 7. Complete Manifolds; Hopf-Rinow and Hadamard Theorems
• 8. Spaces of Constant Curvature
• 9. Variations of Energy
• 10. The Rauch Comparison Theorem
• 11. The Morse Index Theorem
• 12. The Fundamental Group of Manifolds of Negative Curvature
• 13. The Sphere Theorem
• References
• Index

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