Learning objectives
The goal of the course is to give to the students, by means of frontal class, an introduction to 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.
2030 agenda goals for sustainable development
Our aim is to ensure that all students have quality teaching that leads to relevant and effective results
of learning