On equivariant isometric embeddings of Riemannian manifolds with symmetries

Hongda Qiu

paper

On equivariant isometric embeddings of Riemannian manifolds with symmetries

arXiv:2511.09931

Abstract

Let $(M, g)$ be a $C^{\infty}$ -smooth, $n$ -dimensional Riemannian manifold which is diffeomorphic to $\RR^n$ and admit an action of a properly discontinuous and cocompact group. This work proves the existence of a $C^{\infty}$ equivariant isometric embedding of $M$ in some Euclidean space $\RR^q$ where $q = max {s_{n} + 2 n, s_{n} + n + 5}$ is the same as the dimension of Matthias Günther's results.