MATH0464-1 : Differential geometry II

Study Programmes 2016-2017

MATH0464-1

Differential geometry II

Duration :

30h Th, 10h Pr, 20h Mon. WS

Number of credits :

Master in mathematics (120 ECTS)		8
Master in mathematics (60 ECTS)		8

Lecturer :

Pierre Lecomte

Language(s) of instruction :

French language

Organisation and examination :

Teaching in the first semester, review in January

Units courses prerequisite and corequisite :

Prerequisite or corequisite units are presented within each program

Learning unit contents :

Differential equations of order two on manifold and linear connections

On studies the geometrical counter part over a smooth manifold of an ordinary differential equation of order two. Special attention is paid to the case of isochronal equation and their exponential map. This very general concept has many useful particular cases: exponential map of Lie groups, exponential map of matrices, of real or complex numbers, affine maps. It leads to the notion of geodesics. Various charactrizations of a second order differential equation are proposed, among which horizontal distributions on the tangent bundle, the case of linear connection corresponding to isochronal equations that can also be described using covariant derivatives. Flat linear connections are also studied.

Learning outcomes of the learning unit :

Prerequisite knowledge and skills :

Elements of differential geometry.

Planned learning activities and teaching methods :

Mode of delivery (face-to-face ; distance-learning) :

Details are given at the beginning of the academic year.