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arXiv · 2204.04551

The $\kappa$-nullity of Riemannian manifolds and their splitting tensors

Claudio Gorodski·Felippe Guimarães
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Abstract

We consider Riemannian $n$-manifolds $M$ with nontrivial $\kappa$-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 $\kappa$ ($\kappa\in\mathbb R$) 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.

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Claudio Gorodski, Felippe Guimarães. 2022-04-09. The $\kappa$-nullity of Riemannian manifolds and their splitting tensors. https://arxiv.org/abs/2204.04551

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