Extrinsically Symmetric Spaces, Submanifolds of Clifford Type and a Theorem of Harish-Chandra
Abstract
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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Journal of Lie Theory
- Volume
- 36
- Issue
- 1
- Pages
- 23–30
- Publication date
- 17 June 2026
- Language
- EN