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401-2534-00L 6 Credits BSC D-MATH
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Geometry

Geometrie

Lecturers & Examiners: Prof. Dr. Manfred Einsiedler
VVZ CR n/a

Last Updated: 2026-06-01 11:33:47

Abstract

This course gives an introduction into various geometrical topics, such as euclidean, spherical, hyperbolic, and projective geometry. as well as curves and surfaces and their curvature.

Objective

The aim of the lecture is to get an insight into beautiful geometrical results of the last 2000 years and at the same time to gain basics and intuition for further geometry courses, such as differential geometry or algebraic geometry.

Content

The axioms of Euclid and Hilbert; euclidean, spherical, hyperbolic, and projective geometry; isometry groups; curves and surfaces; riemannian metrics; geodesics; Poincaré models of the hyperbolic plane; curvature; Gauss-Bonnet theorem.

Resources

Literature

- P.M.H. Wilson, "Curved Spaces" (main reference) - H. Coxeter, "Introduction to Geometry" - J. McCleary "Geometry from a Differentiable Viewpoint" - M. P. do Carmo "Differential Geometry of Curves and Surfaces"

General Information

Language
German
Levels
BSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 20 minutes

Course Components

Type Title Time & Place Hours
lecture Geometrie
  • Tue 11:15-12:00 (HG D 7.2)
  • Thu 14:15-16:00 (HG G 5)
3 h weekly
exercise Geometrie
Groups are selected in myStudies. Mo 14-16 oder Mo 17-19
  • Mon 14:15-16:00 (HG D 7.1)
  • Mon 17:15-19:00 (HG G 3)
2 h weekly

Offered In