Sumários

Curvature

30 Maio 2018, 11:00 • Susana Duarte Santos

Sectional curvature, Ricci curvature and scalar curvature. Riemannian manifolds with constant sectional curvatures. Isotropic manifolds. Einstein manifolds.

Curvature

25 Maio 2018, 16:00 • Susana Duarte Santos

The curvature endomorphism and curvature tensor: definitions, properties and results concerning local isometry invariants and flat manifolds. Sectional curvature: definition, first properties and geometric meaning.

Affine connections/Curvature

25 Maio 2018, 14:30 • Susana Duarte Santos

Examples related to the theory already developed.
Resolution of exercises.

Geodesics/Curvature

23 Maio 2018, 11:00 • Susana Duarte Santos

Radius functions and distance coordinate systems: consequences.

Curvature: introduction.

Geodesics/Complete Riemannian manifolds

18 Maio 2018, 16:00 • Susana Duarte Santos

Minimizing properties of geodesics (continuation): existence of totally normal neighborhoods and its consequences.

Geodesically complete Riemannian manifolds. Examples. The Riemannian distance function (again). Hopf-Rinow theorem.