Lectures related to Geodesics in general relativity

Explores Killing vectors, conserved quantities, symmetric spaces, and the Riemann curvature tensor properties.

Explores Ruelle resonances for geodesic flows on non-compact manifolds, emphasizing the role of smoothness and eigenvalues in the dynamics.

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Explores the exponential mixing of 3D Anosov flows and their geometric properties, including chaotic behavior and hyperbolic dynamics.

Explores parallel transport along curves and geodesics maximizing proper time between points.

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Explores geodesics as locally shortest paths and defines surface area using parametric squares.

Covers the unit tangent bundle of hyperbolic spaces and geodesic flows.