Comparison Theorems in Riemannian Geometry
Published on 15. January 2009
173 pages
978-0-444-10764-0 (ISBN)
Description
Comparison Theorems in Riemannian Geometry
More details
Content
- Front Cover
- Comparison Theorems in Riemannian Geometry
- Copyright Page
- Contents
- Preface
- Chapter 1. Basic Concepts and Results
- 0. Notation and preliminaries
- 1. First variation of arc length
- 2. Exponential map and normal coordinates
- 3. The Hopf-Rinow Theorem
- 4. The curvature tensor and Jacobi fields
- 5. Conjugate points
- 6. Second variation of arc length
- 7. Submanifolds and the second fundamental form
- 8. Basic index lemmas
- 9. Ricci curvature and Myers' and Bonnet's Theorems
- 10. Rauch Comparison Theorems
- 11. The Cartan-Hadamard Theorem
- 12. The Cartan-Ambrose-Hicks Theorem
- 13. Spaces of constant curvature
- Chapter 2. Toponogov's Theorem
- Chapter 3. Homogeneous spaces
- Chapter 4. Morse theory
- Chapter 5. Closed geodesics and the cut locus
- Chapter 6. The Sphere Theorem and its generalizations
- Chapter 7. The differentiable Sphere Theorem
- Chapter 8. Complete manifolds of nonnegative curvature
- Chapter 9. Compact manifolds of nonpositive curvature
- Index
