Studies

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Inhalt: Auswahl aus folgenden Themen:

  • Einführung in die Differentialgeometrie
  • Metrik und Krümmung
  • Geodäten und Exponentialabbildung und der Satz von Hopf-Rinow
  • Untermanigfaltigkeiten Euklidischen Räume
  • Räume konstanter Krümmung
  • Zusammenhänge zwischen Krümmung und Topologie (z. B. Satz von Myers, Hadamard-Cartan, Klingenberg, Starrheitssätze, Bishop-Gromov)

Literatur (weitere Literatur wird in der Vorlesung bekannt gegeben)

  • Isaac Chavel, Riemannian geometry: a modern introduction

Contents: A selection of the following topics

  • Introduction to differential geometry
  • Connections, metrics and curvature
  • Geodesics, the exponential map and the Theorem of Hopf-Rinow
  • Submanifolds of Euclidean space
  • Spaces of constant curvature
  • Relationship between curvature and Topology (e.g. Theorems of Myers, Hadamard-Cartan, Klingenberg, Bishop-Gromov)

Literatur (further literature will be given in the lecture)

  • Isaac Chavel, Riemannian geometry: a modern introduction

Cross-language

192 143
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