## Riemannian GeometryWalter de Gruyter, 3 de mai. de 2011 - 419 páginas The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) |

### Conteúdo

1 | |

8 | |

13 | |

23 | |

31 | |

15 Covariant Derivation | 39 |

16 The Exponential Mapping | 53 |

17 Lie Groups | 59 |

25 Appendix The S1 and the Z2action on AM | 196 |

26 Index and Curvature | 203 |

26 Appendix The Injectivity Radius for 14pinched Manifolds | 212 |

27 Comparison Theorems for Triangles | 215 |

28 The Sphere Theorem | 229 |

29 Noncompact Manifolds of Positive Curvature | 240 |

Structure of the Geodesic Flow | 256 |

32 Properties of the Geodesic Flow | 265 |

18 Riemannian Manifolds | 67 |

19 Geodesics and Convex Neighborhoods | 78 |

110 Isometric Immersions | 86 |

111 Riemannian Curvature | 97 |

112 Jacobi Fields | 109 |

Curvature and Topology | 124 |

21 Appendix Orientation | 136 |

22 Symmetric Spaces | 141 |

23 The Hilbert Manifold of H1curves | 158 |

24 The Loop Space and the Space of Closed Curves | 170 |

25 The Second Order Neighborhood of a Critical Point | 181 |

33 Stable and Unstable Motions | 279 |

34 Geodesics on Surfaces | 288 |

35 Geodesics on the Ellipsoid | 303 |

36 Closed Geodesies on Spheres | 324 |

37 The Theorem of the Three Closed Geodesics | 337 |

38 Manifolds of NonPositive Curvature | 350 |

39 The Geodesic Flow on Manifolds of Negative Curvature | 363 |

310 The Main Theorem for Surfaces of Genus 0 | 380 |

References | 393 |

403 | |