What question did this study set out to answer?

The main goal is to establish the existence of a specific type of embedding for Riemannian manifolds with symmetries.

February 2, 2026

On equivariant isometric embeddings of Riemannian manifolds with symmetries

HQHongda QiuPennsylvania State University

Puntos clave

The main goal is to establish the existence of a specific type of embedding for Riemannian manifolds with symmetries.
Consider a smooth Riemannian manifold with specific group actions.
Utilize techniques from differential geometry and group theory.
Prove the existence of an embedding using mathematical analysis.
Demonstrated existence of an equivariant isometric embedding.
Showed that the embedding is optimal in terms of dimension bound.
Connected findings to previous results by Matthias Günther.

Resumen

Let Formula: see text be a Formula: see text-smooth, Formula: see text-dimensional Riemannian manifold that is diffeomorphic to Formula: see text and admits a properly discontinuous, cocompact, isometric, fixed-point-free action by a group. This work proves the existence of a Formula: see text equivariant isometric embedding of Formula: see text into some Euclidean space Formula: see text with Formula: see text which is the same as the optimal dimension bound in Matthias GÃ¼nther’s results.

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