Credits: 7.5

Type: bridging

Objectives:

• To provide an initial look at the geometry of differentiable manifolds.
• To study vector fields tangent to a manifold and vector field flows, as well as their connections and other derivatives.
• To introduce the fundamental concepts of a Riemannian metric.

Knowledge:

• Differentiable manifolds and submanifolds.
• Vector fields and flows.
• Connections and parallel transport.
• Riemannian manifolds.
• Curvature.
• Geodesics and geodesic distance.

Subject-specific competences:

• To understand and use the basic tools applied to differentiable manifolds of any dimension.
• To distinguish between the concepts of differential geometry that rely on the choice of a Riemannian metric and the concepts that do not.
• To be able to calculate the curvature and the geodesics in Riemannian manifolds.