Infinite-dimensional geometry: Sprays and covariant derivatives vs. weak Riemannian metrics
Channel: Alexander Schmeding
Date: 2020-11-13

In this short lecture we recall properties of strong and weak Riemannian metrics. For weak Riemannian metrics we shall see that it is not alway possible to find an associated covariant derivative. This leads to several approaches of strengthening the weak setting by requiring additional properties (leading to so called robust Riemannian metrics and (co-)orthogonal structures).

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/).