An explicit formula for the Laplace-Beltrami operator on the Stiefel manifold

Fuente: arXiv
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Hauptverfasser: Birtea, Petre, Casu, Ioan, Comanescu, Dan
Format: Preprint
Veröffentlicht: 2025
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author Birtea, Petre
Casu, Ioan
Comanescu, Dan
author_facet Birtea, Petre
Casu, Ioan
Comanescu, Dan
contents We derive an explicit formula for the Laplace-Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework of Laplace operators on constraint manifolds, we provide the formula for the Laplace-Beltrami operator in terms of the ambient Euclidean coordinates. The result extends previously known cases, recovering the formulas for the sphere and the special orthogonal group as particular instances.
format Preprint
id arxiv_https___arxiv_org_abs_2509_18877
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An explicit formula for the Laplace-Beltrami operator on the Stiefel manifold
Birtea, Petre
Casu, Ioan
Comanescu, Dan
Differential Geometry
Mathematical Physics
53C30, 15B10, 53Bxx, 58Cxx
We derive an explicit formula for the Laplace-Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework of Laplace operators on constraint manifolds, we provide the formula for the Laplace-Beltrami operator in terms of the ambient Euclidean coordinates. The result extends previously known cases, recovering the formulas for the sphere and the special orthogonal group as particular instances.
title An explicit formula for the Laplace-Beltrami operator on the Stiefel manifold
topic Differential Geometry
Mathematical Physics
53C30, 15B10, 53Bxx, 58Cxx
url https://arxiv.org/abs/2509.18877