3 problems

Let $\mathcal{M}:=(M,g)$ be a pseudo-Riemannian manifold of Lorentzian signature $(1,q)$. For $P\in M$, let $g_P:=g|_{T_PM}$ and let $\nabla^iR_P:=\nabla^iR|_{T_PM}$. Its $k$-model…

Let $s_{p,q}$ be a number depending on the signature $(p,q)$ such that an $SCH_{s_{p,q}}(1,3)$ manifold is locally homogeneous, and let $k_{p,q}$ denote the corresponding finite Si…

For a curvature homogeneous Lorentzian manifold, let $k_{a,b}$ denote the relevant curvature-homogeneity bound, with $k_{1,3}$ its value in the four-dimensional case considered her…