Infinite-dimensional geometry 4.3.: Geodesics, sprays and covariant derivatives, Part I: sprays
Channel: Alexander Schmeding
Date: 2020-11-12

We introduce the concept of second order vector field and spray on a manifold. This allows us to give a first definition of a geodesic as a solution to a second order differential equation described by a spray.

This is part of the course MAT331: Topics in Analysis at the University of Bergen in Fall 2020. 
This course (and the lecture) was supported by Trond Mohn foundation within the Pure Mathematics in Norway program (https://www.puremath.no/).