An explicit formula for the Laplace-Beltrami operator on the Stiefel manifold
Differential Geometry
2025-10-15 v2 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.2509.18877,
title = {An explicit formula for the Laplace-Beltrami operator on the Stiefel manifold},
author = {Petre Birtea and Ioan Casu and Dan Comanescu},
journal= {arXiv preprint arXiv:2509.18877},
year = {2025}
}