Comparison Theorems in Riemannian Geometry
Cheeger, Jeff.
Comparison Theorems in Riemannian Geometry [electronic resource] / Jeff Cheeger and David G. Ebin. - Burlington : Elsevier Science, 2009. - 1 online resource (183 pages). - North-Holland Mathematical Library . - North-Holland mathematical library. .
Front Cover; Comparison Theorems in Riemannian Geometry; Copyright Page; Preface; Contents; 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 curvatureChapter 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.
Comparison Theorems in Riemannian Geometry.
9780444107640 (electronic bk.) 0444107649 (electronic bk.)
Geometry, Riemannian.
Riemannian manifolds.
MATHEMATICS--Transformations.
Geometry, Riemannian.
Riemannian manifolds.
Electronic books.
QA649 / .C47 2009
515.73 516.3/73 516.373
Comparison Theorems in Riemannian Geometry [electronic resource] / Jeff Cheeger and David G. Ebin. - Burlington : Elsevier Science, 2009. - 1 online resource (183 pages). - North-Holland Mathematical Library . - North-Holland mathematical library. .
Front Cover; Comparison Theorems in Riemannian Geometry; Copyright Page; Preface; Contents; 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 curvatureChapter 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.
Comparison Theorems in Riemannian Geometry.
9780444107640 (electronic bk.) 0444107649 (electronic bk.)
Geometry, Riemannian.
Riemannian manifolds.
MATHEMATICS--Transformations.
Geometry, Riemannian.
Riemannian manifolds.
Electronic books.
QA649 / .C47 2009
515.73 516.3/73 516.373
