Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
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401-3532-08L  Differential Geometry II

SemesterSpring Semester 2017
LecturersU. Lang
Periodicityyearly recurring course
Language of instructionEnglish


AbstractIntroduction 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.
ObjectiveThe aim of this course is to give an introduction to Riemannian Geometry in combination with some elements of modern metric geometry.
ContentRiemannian 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.
LiteratureRiemannian 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 / NoticePrerequisite is a working knowledge of elementary differential geometry (curves and surfaces in Euclidean space), differentiable manifolds, tangent and tensor bundles, and differential forms.