Riemannian geometry in infinite dimensional spaces

TL;DR

This paper establishes foundational concepts of Riemannian geometry in infinite-dimensional spaces, providing essential groundwork for further research in related geometric structures.

Contribution

It introduces fundamental principles of Riemannian geometry in infinite-dimensional contexts, enabling future exploration of isometries in Kähler metric spaces.

Findings

Established basic geometric structures in infinite-dimensional spaces

Provided tools for analyzing isometries in Kähler metrics

Laid groundwork for subsequent detailed studies

Abstract

We lay foundations of the subject in the title, on which we build in another paper devoted to isometries in spaces of K\"ahler metrics.