MM865: Riemannian Geometry

Entry requirements

MM865 cannot be taken, if MM564 has been passed

Academic preconditions

Students taking the course are expected to:

Have knowledge of the contents of MM536
Have knowledge of the contents of MM540 or MM505
Have knowledge of the contents of MM533
Knowledge of MM512 is recommended but not required

Course introduction

The aim of the course is to obtain knowledge about Riemannian manifolds, methods and tools of differential geometry. The student is enabled :

to analyse, apply and modify these techniques by means of mathematical analysis
to formulate the problems (including proofs) in a correct mathematical language
to make use of these techniques in new problem settings

The course builds on the knowledge acquired in the Bachelor program. The course has connections to MM512: Curves and Surfaces. The course gives an academic basis for Master theses.

In relation to the competence profile of the degree it is the explicit focus of the course to:

Give the competence to analyse and apply mathematical models
Give basic understanding on how to work with geometric ideas and manifold structures

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

understand the basic principles of Riemannian geometry
understand and work manifolds, tangent spaces and curvature
compare and contrast the methods introduced in the course
transfer the learning content to new problems and applications

Content

The following main topics are contained in the course:

Topological and differential manifolds
Tangent spaces
Riemannian metrics
Covariant derivatives
Geodesics
Curvature

Literature

See Itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

January

Tests

Oral examination

EKA

N310079102

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Student Identification Card

Language

Normally, the same as teaching language

Examination aids

To be announced during the course.

ECTS value

Indicative number of lessons

70 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase. These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:

Intro phase (lectures) - 56 hours
Training phase: 14 hours, including 14 hours tutorials

Teaching is centred on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.

Activities during the studyphase:

Reading of suggested literature
Preparation of exercises in study groups
Contributing to online learning activities related to the course

Teacher responsible

Name	E-mail	Department
Jørgen Ellegaard Andersen	jea@sdu.dk	Quantum Mathematics

Additional teachers

Name	E-mail	Department	City
Konstantin Wernli	kwernli@imada.sdu.dk	Quantum Mathematics

Timetable

Odense

Show full time table

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile	Education	Semester	Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study.

If a transitional arrangement has been made for a course, it will be stated in the list.

See transitional arrangements for all courses at the Faculty of Science.