DIFFERENTIAL GEOMETRY
cod. 00474

Academic year 2024/25
2° year of course - Second semester
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

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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