General Relativity and Sectional Curvature

A discussion is given of the sectional curvature function on a four-dimensional Lorentz manifold and, in particular, on the space-time of Einstein's general relativity theory. Its tight relationship to the metric tensor is demonstrated and some of its geometrical and algebraic properties evaluated. The concept of a sectional curvature preserving symmetry, in the form of a certain smooth vector field, is introduced and discussed.