论文标题
在笛卡尔坐标的正交集团上的Laplace-Beltrami操作员
Laplace-Beltrami operator on the orthogonal group in Cartesian coordinates
论文作者
论文摘要
使用嵌入式梯度矢量场方法（请参阅P. Birtea，D。Comanescu，Hessian Operators on Constraint Primolds，J。Nonlinear Science 25，2015），我们为Laplace-Beltrami操作员提供了一个通用公式，该公式定义在约束歧管上，写在环境坐标中。关于$ n \ times n $矩阵的正交组作为欧几里得空间的约束子曼群，我们使用环境欧几里得辅助物为正交组上的laplace-beltrami操作员提供了明确的公式。我们将此新公式应用于某些相关功能。
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.
