240071 Differentialgeometrie (G&T 2) (V) (WiSe 2023/2024)
Contents, comment
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1. Mannigfaltigkeiten: Differenzierbare Strukturen, Tangentialraum, Kotangentialraum, Untermannigfaltigkeiten, Riemannsche Metriken.
2. Flächen: Flächen im dreidimensionalen euklidischen Raum, Fundamentalformen, Gauß-Krümmung, Riemannsche Flächen, Riemannsche Krümmung, Theorema Egregium.
3. Differentialkalkül: Derivation, kovariante Ableitung, Lie-Ableitung, äußere Ableitung, Krümmungsform, de Rham Kohomologie.
4. Differenzierbare Bündel: Zusammenhänge, Krümmungstensor, Levi-Civita-Zusammenhang.
5. Integralsätze für Krümmungsterme.
Requirements for participation, required level
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Notwendig: Analysis 2, Lineare Algebra 2.
Hilfreich: Geometrie und Topologie 1.
Bibliography
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Bär, Christian: Elementare Differentialgeometrie.
Berger, Marcel: A Panoramic View of Riemannian Geometry.
de Rham, Georges: Differentiable Manifolds.
Kobayashi, Shoshichi: Differential Geometry of Curves and Surfaces.
Kühnel, Wolfgang: Differentialgeometrie.
Teaching staff
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| Degree programme/academic programme | Validity | Variant | Subdivision | Status | Semester | LP | |
|---|---|---|---|---|---|---|---|
| Studieren ab 50 |
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