Some general, algebraic remarks on tensor classification, the group $O(2,2)$ and sectional curvature in 4-dimensional manifolds of neutral signature

Abstract

This paper presents a general discussion of the geometry of a manifold $M$ of dimension $4$ which admits a metric $g$ of neutral signature $(+,+,-,-)$. The tangent space geometry at $m\in M$, the complete pointwise algebraic classification of second order