On equivariant isometric embeddings of Riemannian manifolds with symmetries

2025/11/13 by Qiu, Hongda
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.09931

Abstract

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

Citations

• On the geometry of Riemannian isometric embeddings
• Equivariant embeddings of manifolds into Euclidean spaces
• Equivariant embeddings of Hermitian symmetric spaces
• Gunther's proof of Nash's isometric embedding theorem

Related

• On the geometry of Riemannian isometric embeddings
• Equivariant embeddings of manifolds into Euclidean spaces
• C¹-isometric embeddings of Riemannian spaces in Lorentzian spaces
• Universal Embedding spaces for G-manifolds
• C^1,1-ε Isometric embeddings