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401-3531-00L 11 Credits BSC , MSC D-PHYS , D-MATH

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Differential Geometry I

Differentialgeometrie I

Lecturers & Examiners: Prof. Dr. Tom Ilmanen

VVZ CR n/a

Last Updated: 2026-02-05 15:24:27

Abstract

Differentiable manifolds, tangent bundle, immersions and embeddings, Riemannian metrics, connections, vector bundles, Riemannian curvature, hyperbolic space, extrinsic curvature, some Lie groups.

Objective

Introduction to differential geometry and differential topology.

Content

Diff Geom I: Differentiable manifolds, tangent bundle, immersions and embeddings, Riemannian metrics, connections, vector bundles, Riemannian curvature, hyperbolic space, extrinsic curvature, some Lie groups. Diff Geom II: Differential forms, Stokes' theorem, de Rham cohomology, Hodge theory, geometric interpretations. Possibly: Sard's theorem, transversality, degree and intersection number.

General Information

Language: English (lecture), German (exercise)
Levels: BSC , MSC
Frequency: Yearly recurring

Examination

Type: session examination
Mode: oral 30 minutes

Course Components