KNOWLEDGE AND UNDERSTANDING: becoming familiar with key results
of Riemannian geometry

APPLYING KNOWLEDGE AND UNDERSTANDING: developing the ability to
solve independently exercises in Riemannian geometry

MAKING JUDGEMENTS: recognising and applying the basic techniques of
Riemannian grometry

COMMUNICATION SKILLS: achieving proficiency in the language of
Riemannian geometry

LEARNING SKILLS: developing the ability to use with profit the main
textbooks.

Real calculus in several variables. General and algebraic topology with particular attention ro coverings and deck transformations. Basic notions of the geoemtry of curves and surfaces.

Il corso si prefigge di fornire allo studente le conoscenze di base in Geometria Riemanniana.

M. P. do Carmo, Riemannian geometry, Birkhäuser.

Bozza sintetica di contenuti del corso: Varietà Differenziabili Spazio Tangente Fibrato Tangente Metriche e Varietà Riemanniane La connessione di Levi-Civita. Geodetiche Il tensore di Curvatura. Curvatura e Geometria Locale. Campi di Jacobi. Varietà Complete e applicazioni. Equazioni fondamentali e Teoremi di Confronto.

The course consists of lectures during which the Instructor discusses all
the details of the topics covered, answers student's questions and tries to
get them involved.

Ulteriori informazioni potranno essere eventualmente reperibili nella pagina Moodle del corso.

Oral exam