# Short survey on the existence of slices for the space of Riemannian metrics

## TL;DR

This paper reviews the slice theorem for the action of diffeomorphisms on Riemannian metrics, discusses recent advances, and offers a more concise proof of slice existence.

## Contribution

It provides a concise proof of the slice theorem and summarizes recent developments in the study of Riemannian metric spaces.

## Key findings

- Confirmed the existence of slices for the space of Riemannian metrics
- Summarized recent progress in the field
- Presented a simplified proof of the slice theorem

## Abstract

We review the well-known slice theorem of Ebin for the action of the diffeomorphism group on the space of Riemannian metrics of a closed manifold. We present advances in the study of the spaces of Riemannian metrics, and produce a more concise proof for the existence of slices.