We prove that a compact, intrinsically symmetric submanifold of an 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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Keywords: extrinsically symmetric spaces, Clifford tori, Clifford type, strongly orthogonal roots
Eschenburg, Jost-Hinrich 1 ; Heintze, Ernst 1 ; Quast, Peter 1
Eschenburg, Jost-Hinrich; Heintze, Ernst; Quast, Peter. Extrinsically Symmetric Spaces, Submanifolds of Clifford Type and a Theorem of Harish-Chandra. Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 23-30. doi: 10.5802/jolt.1416
@article{10_5802_jolt_1416,
author = {Eschenburg, Jost-Hinrich and Heintze, Ernst and Quast, Peter},
title = {Extrinsically {Symmetric} {Spaces,} {Submanifolds} of {Clifford} {Type} and a {Theorem} of {Harish-Chandra}},
journal = {Journal of Lie Theory},
pages = {23--30},
year = {2026},
publisher = {XXXX},
volume = {36},
number = {1},
doi = {10.5802/jolt.1416},
language = {en},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1416/}
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TY - JOUR AU - Eschenburg, Jost-Hinrich AU - Heintze, Ernst AU - Quast, Peter TI - Extrinsically Symmetric Spaces, Submanifolds of Clifford Type and a Theorem of Harish-Chandra JO - Journal of Lie Theory PY - 2026 SP - 23 EP - 30 VL - 36 IS - 1 PB - XXXX UR - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1416/ DO - 10.5802/jolt.1416 LA - en ID - 10_5802_jolt_1416 ER -
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