Mathematics | University of Parma

Professor
Academic discipline: Geometria (MAT/03)
Field: Attività formative affini o integrative
Type of training activity: Related/supplementary

48 hours
of face-to-face activities

6 credits

hub:

course unit
in ITALIAN

lectures timetable unavailable

exam calls

Learning objectives

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 unit content

RIEMANNIAN GEOMETRY

Full programme

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

Bibliography

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.

Other information

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DIFFERENTIAL GEOMETRY cod. 00474