论文标题
Einstein-Hilbert型动作几乎是$ K $ - 产品歧管
The Einstein-Hilbert type action on almost $k$-product manifolds
论文作者
论文摘要
赋予$ k> 2 $正交补充分布（在这里称为Riemannian几乎$ k $ prododuct结构）的Riemannian歧管出现在诸如Multiply Warped产品，由几个叶子组成的网和正确的Dupin Hypersurfaces组成的主题中。在本文中，我们考虑了$ k> 2 $的这种结构的混合标量曲率，从适应于适应的度量的einstein-hilbert型动作中得出Euler-lagrange方程，并以爱因斯坦方程的不错形式呈现它们。
A Riemannian manifold endowed with $k>2$ orthogonal complementary distributions (called here a Riemannian almost $k$-product structure) appears in such topics as multiply warped products, the webs composed of several foliations, and proper Dupin hypersurfaces of real space-forms. In the paper, we consider the mixed scalar curvature of such structure for $k>2$, derive Euler-Lagrange equations for the Einstein-Hilbert type action with respect to adapted variations of metric, and present them in a nice form of Einstein equation.
