61467 - Differential Geometry (2018/2019)

General information

61467 - Differential Geometry (GD, 7 CFU), second semester, years: 3° LT.

Course content

Topological, differentiable and riemannian manifolds. Differentiable maps. Tangent and cotangent bundles. Tensor algebra. Vector fields and their flows; Lie derivative. Differential forms; de Rham complex. Orientable manifolds.  Riemannian metrics.Curves and surfaces in tridimentional Euclidean space.Gauss curvature and theorema egregium. Surfaces of constant curvature. Covariant derivative and Riemann curvature tensor; geodesics. Normal coordinates.  Lie groups and their Lie algebras; exponenential maps.

Language

Italian

Teacher

Claudio Bartocci

Teaching style

In presence

Attendance

Suggested