# Urs Lang: Catalogue data in Spring Semester 2017

Name | Prof. Dr. Urs Lang |

Field | Mathematik |

Address | Professur für Mathematik ETH Zürich, HG G 27.3 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 60 11 |

urs.lang@math.ethz.ch | |

URL | http://www.math.ethz.ch/~lang |

Department | Mathematics |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-3532-08L | Differential Geometry II | 10 credits | 4V + 1U | U. Lang | |

Abstract | Introduction to Riemannian Geometry in combination with some elements of modern metric geometry. Contents: Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, curvature and topology, spaces of riemannian manifolds. | ||||

Objective | The aim of this course is to give an introduction to Riemannian Geometry in combination with some elements of modern metric geometry. | ||||

Content | Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form of submanifolds, riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, relations between curvature and topology, spaces of riemannian manifolds. | ||||

Literature | Riemannian Geometry: - M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992 - S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer 2004 - B. O'Neill, Semi-Riemannian Geometry, With Applications to Relativity, Academic Press 1983 Metric Geometry: - M. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer 1999 - D. Burago, Y. Burago, S. Ivanov, A Course in Metric Geometry, Amer. Math. Soc. 2001 | ||||

Prerequisites / Notice | Prerequisite is a working knowledge of elementary differential geometry (curves and surfaces in Euclidean space), differentiable manifolds, tangent and tensor bundles, and differential forms. | ||||

401-5530-00L | Geometry Seminar | 0 credits | 1K | M. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, University lecturers | |

Abstract | Research colloquium | ||||

Objective |