论文标题
公制植物几乎产物歧管上的变分问题
Variational problem on a metric-affine almost product manifold
论文作者
论文摘要
We study a variational problem on a smooth manifold with a decomposition of the tangent bundle into $k>2$ subbundles (distributions), namely, we consider the integrated sum of their mixed scalar curvatures as a functional of adapted pseudo-Riemannian metric (keeping the pairwise orthogonality of the distributions) and contorsion tensor, defining a linear connection.这种功能使我们从以下意义上概括了爱因斯坦指标类别：如果所有分布都是一维的，那么它与爱因斯坦 - 希尔伯特（Einstein-Hilbert）作用的几何部分相吻合，仅限于改编的指标。我们证明，对我们功能至关重要的成对度量指标使所有分布都完全脐带。在某些特殊情况下，我们获得了这些关键对存在的例子和障碍：具有统计联系的扭曲产品；半对称性连接和带有度量兼容连接的3 sasaki歧管。
We study a variational problem on a smooth manifold with a decomposition of the tangent bundle into $k>2$ subbundles (distributions), namely, we consider the integrated sum of their mixed scalar curvatures as a functional of adapted pseudo-Riemannian metric (keeping the pairwise orthogonality of the distributions) and contorsion tensor, defining a linear connection. This functional allows us to generalize the class of Einstein metrics in the following sense: if all of the distributions are one-dimensional, then it coincides with the geometrical part of the Einstein-Hilbert action restricted to adapted metrics. We prove that metrics in pairs metric-contorsion critical for our functional make all of the distributions totally umbilical. We obtain examples and obstructions to existence of those critical pairs in some special cases: twisted products with statistical connections; semi-symmetric connections and 3-Sasaki manifolds with metric-compatible connections.
