论文标题
$κ$ - riemannian歧管及其分裂张量
The $κ$-nullity of Riemannian manifolds and their splitting tensors
论文作者
论文摘要
我们考虑riemannian $ n $ - manifolds $ m $，其曲率张量$ r $的非平凡$κ$ -Nullity“分布”，即，切线子空间的变量排名分布到$ m $，其中$ r $与courvate curvator curvator curvator curvature Is $κ$ ch $κ$κ$κ\κ\ brb com coss coss $ r $ cosefliss $ r $ coss coss $ r $ coss。我们在不同的其他假设下获得了分类定理，从低效率/结合性，受控标量曲率或有限体积的商的存在方面获得了分类定理。我们证明了新的结果，但也重新审视了以前的结果。
We consider Riemannian $n$-manifolds $M$ with nontrivial $κ$-nullity "distribution" of the curvature tensor $R$, namely, the variable rank distribution of tangent subspaces to $M$ where $R$ coincides with the curvature tensor of a space of constant curvature $κ$ ($κ\in\mathbb R$) is nontrivial. We obtain classification theorems under diferent additional assumptions, in terms of low nullity/conullity, controlled scalar curvature or existence of quotients of finite volume. We prove new results, but also revisit previous ones.
