PHYSICS

Master Degree

DIFFERENTIAL GEOMETRY

Teachers: 
BILIOTTI Leonardo
Credits: 
6
Site: 
PARMA
Year of erogation: 
2020/2021
Unit Coordinator: 
Disciplinary Sector: 
GEOMETRY
Semester: 
Second semester
Language of instruction: 

Italian

Learning outcomes of the course unit

The goal of the course is to give to the students, by means of frontal class, an introduction to Riemannian Geometry.

Prerequisites

DIFFERENTIAL GEOMETRY

Course contents summary

RIEMANNIAN GEOMETRY

Course contents

Riemannian metrics, Affine connections, Riemannian connections, geodesics, minimizing properties of geodesics, convex neighborhoods, curvatura, sectional curvature, Ricci curvature, Jacobi equation, conjugate points, Hopf-Rinow's Theorem, Theorem of Hadamard, Bochner techniques, Theorem of Bonnet-Meyer, Theorem of Synge, The Morse index Theorem

Recommended readings

ALEXANDRINO, BETTIOL ''LIE GROUPS AND GEOMETRICAL ASPECTS OF ISOMETRIC ACTIONS, MANFREDO DO CARMO ''RIEMANNIAN GEOMETRY''

Teaching methods

The course counts 9CFUs which corresponds to 48 hours of lectures. The didactic activities is given by frontal class.

Assessment methods and criteria

Verification of the knowledges is achieved by an oral exam.