Dettagli sull'Insegnamento per l'A.A. 2019/2020

Prerequisiti

Analysis of one and many variables, linear algebra, geometry of curves and surfaces, basic topology.

Obiettivi

The objective of this course is to get the student familiar with basic notions and some fundamental results of Riemannian Geometry . At the end of the course the student should be able to solve by her/him-self some simple, but new problems regarding all the program.

Sillabo

• Differentiable manifolds
• Riemannian Metrics
• Affine and Riemannian connections
• Geodesics, curvatures
• Jacobi Fields
• Isometric Immersions
• Complete manifolds: Hopf and Hadamard theorems
• Constan curvature spaces
• Variations of energy

Descrittori di Dublino

Alla fine del corso, lo studente dovrebbe

Testi di riferimento

• M.P. Do Carmo, Riemannian Geometry , Birkhauser. 1992.    
• P. Petersen, Riemannian Geometry , Springer 2016.    

Modalità d'esame

Written and Oral

Note

• The objective of the course is to give the basic notion Riemannian Geoemtry and to be able to understand some fundamental results of the subject.

Risorse Internet

Aggiornamenti alla pagina del corso

• A.A. 2015/2016
• A.A. 2016/2017
• A.A. 2017/2018
• A.A. 2018/2019
• A.A. 2019/2020