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, 2026Journal of Topology and Analysis

On equivariant isometric embeddings of Riemannian manifolds with symmetries

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HQHongda QiuPennsylvania State University

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Implication

This work proves the existence of an equivariant isometric embedding in Euclidean space, indicating a strong connection between geometry and group actions.

Key Points

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.

Cite This Study

Hongda Qiu (2026) studied this question.

synapsesocial.com/papers/6980fe35c1c9540dea8101ac https://doi.org/10.1142/s1793525326500214

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Implication

This work proves the existence of an equivariant isometric embedding in Euclidean space, indicating a strong connection between geometry and group actions.

On equivariant isometric embeddings of Riemannian manifolds with symmetries

Discussion

Member takes

Implication

Key Points

Cite This Study

On equivariant isometric embeddings of Riemannian manifolds with symmetries

Discussion

Member takes

Implication

Key Points

Cite This Study

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