论文标题
Leibniz的共同体学和可区分流形的联系
Leibniz Cohomology and Connections on Differentiable Manifolds
论文作者
论文摘要
我们展示了Riemannian歧管上的仿射连接如何自然地作为科链作为科链，用于矢量场的Leibniz leibniz共同体，具有系数在伴随表示中。 Levi-Civita连接的Leibniz串联可以表示为两个术语的总和，一个是Laplace-Beltrami操作员，另一个是RICCI曲率术语。该共核的消失在Laplacian的本征界方面具有解释。此外，我们用欧几里得$ {\ bf {r}}^n $在欧几里得属上的某个矢量场的伴随系数计算Leibniz共同体，该系数对应于offine orthoconal lie代数，$ n \ geq 3 $。
We show how an affine connection on a Riemannian manifold occurs naturally as a cochain in the complex for Leibniz cohomology of vector fields with coefficients in the adjoint representation. The Leibniz coboundary of the Levi-Civita connection can be expressed as a sum of two terms, one the Laplace-Beltrami operator and the other a Ricci curvature term. The vanishing of this coboundary has an interpretation in terms of eigenfunctions of the Laplacian. Additionally, we compute the Leibniz cohomology with adjoint coefficients for a certain family of vector fields on Euclidean ${\bf{R}}^n$ corresponding to the affine orthogonal Lie algebra, $n \geq 3$.
