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arXiv · 2206.06790

Laplace-Beltrami operator on the orthogonal group in Cartesian coordinates

Petre Birtea·Ioan Casu·Dan Comanescu
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Abstract

Using the embedded gradient vector field method (see P. Birtea, D. Comanescu, Hessian operators on constraint manifolds, J. Nonlinear Science 25, 2015), we present a general formula for the Laplace-Beltrami operator defined on a constraint manifold, written in the ambient coordinates. Regarding the orthogonal group as a constraint submanifold of the Euclidean space of $n\times n$ matrices, we give an explicit formula for the Laplace-Beltrami operator on the orthogonal group using the ambient Euclidean coordinates. We apply this new formula for some relevant functions.

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Petre Birtea, Ioan Casu, Dan Comanescu. 2022-06-14. Laplace-Beltrami operator on the orthogonal group in Cartesian coordinates. https://doi.org/10.1016/j.acha.2023.101619

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