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arXiv · 2502.18967

Extrinsically Symmetric Spaces, Submanifolds of Clifford Type and a Theorem of Harish-Chandra

Jost-Hinrich Eschenburg·Ernst Heintze·Peter Quast
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Abstract

We prove that a compact, intrinsically symmetric submanifold of a Euclidean space is extrinsically symmetric if and only if its maximal tori are Clifford tori in the ambient space. Moreover, we show that this result can be used to give a geometric proof of a result of Harish-Chandra on strongly orthogonal roots in semisimple Lie algebras.

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Jost-Hinrich Eschenburg, Ernst Heintze, Peter Quast. 2025-02-26. Extrinsically Symmetric Spaces, Submanifolds of Clifford Type and a Theorem of Harish-Chandra. https://arxiv.org/abs/2502.18967

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