October 20, 2025Open Access

Almost symmetric submanifolds

Key Points

Almost symmetric submanifolds in Euclidean space exhibit structural uniqueness based on cohomogeneity.
The cohomogeneity of these submanifolds is proven to be at most one, establishing a key classification metric.
The study connects almost symmetric submanifolds closely with symmetric submanifolds and sub-Riemannian spaces.
New results about their structure contribute significantly to the understanding of submanifold classification.

Abstract

We introduce the class of almost symmetric submanifolds of Euclidean space, a close relative of symmetric submanifolds and (contact) sub-Riemannian symmetric spaces, and prove a number of results about their structure and classification. In particular, we show that their cohomogeneity is at most one.

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Cite This Study

Gorodski et al. (Sat,) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac36588 https://doi.org/https://doi.org/10.48550/arxiv.2509.23301

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