401-3531-00L  Differential Geometry I

SemesterAutumn Semester 2019
LecturersU. Lang
Periodicityyearly recurring course
Language of instructionEnglish
CommentAt most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics.



Courses

NumberTitleHoursLecturers
401-3531-00 VDifferential Geometry I4 hrs
Mon13:15-15:00ML H 44 »
Wed13:15-15:00HG G 5 »
U. Lang
401-3531-00 UDifferential Geometry I
Groups are selected in myStudies.
Thu 14-15 or Thu 15-16 or Fri 13-14
1 hrs
Thu14:15-15:00HG E 21 »
15:15-16:00HG F 26.5 »
Fri13:15-14:00HG F 3 »
U. Lang

Catalogue data

AbstractIntroduction to differential geometry and differential topology. Contents: Curves, (hyper-)surfaces in R^n, geodesics, curvature, Theorema Egregium, Theorem of Gauss-Bonnet. Hyperbolic space. Differentiable manifolds, immersions and embeddings, Sard's Theorem, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem.
Objective
Lecture notesPartial lecture notes are available from Link
LiteratureDifferential geometry in R^n:
- Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces
- Wolfgang Kühnel: Differentialgeometrie. Kurven-Flächen-Mannigfaltigkeiten
- Christian Bär: Elementare Differentialgeometrie
Differential topology:
- Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds
- Victor Guillemin & Alan Pollack: Differential Topology
- Morris W. Hirsch: Differential Topology

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits10 credits
ExaminersU. Lang
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 180 minutes
Written aidsNone
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
Main linkInformation
Only public learning materials are listed.

Groups

401-3531-00 UDifferential Geometry I
GroupsG-01
Thu14:15-15:00HG E 21 »
G-02
Thu15:15-16:00HG F 26.5 »
G-03
Fri13:15-14:00HG F 3 »

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
High-Energy Physics (Joint Master with EP Paris)Optional Subjects in MathematicsWInformation
Mathematics BachelorCore Courses: Pure MathematicsWInformation
Mathematics MasterBachelor Core Courses: Pure MathematicsE-Information
Physics BachelorSelection of Higher Semester CoursesWInformation
Physics MasterSelection: MathematicsWInformation