I will give an overview of infinite-dimensional Riemannian geometry, especially those arising in physical applications. In particular I will discuss the sign of the curvature for the volume-preserving diffeomorphisms and the space of inextensible strings, and what it means. The talk will assume some knowledge of finite-dimensional Riemannian geometry but not much beyond that.
Curvatures of infinite-dimensional manifolds -Part I
Curvatures of infinite-dimensional manifolds -Part I