Evens and Mids

On a 3-dimensional Lorentzian manifold, the sectional curvature function at any point may be represented as a rational function (quotient of two quadratics) on the real projective plane [2]. (More generally, the sectional curvature at a point of any pseudoRiemannian n-manifold may be represented as a rational function on the Grassmann variety of planes in n-space.) Using this representation, Beem and I [1] were able to generalize and/or rederive all previously known results on the values of pseudoriemannian sectional curvature in all dimensions ≥ 3. L. Cordero and I decided to work with this representation. We proposed that I spend a semester at Santiago de Compostela supported by the Spanish DGICYT, and it was approved for January-June 1991. During this period we produced three papers on the 3-dimensional problem. In [2] we determined the possible symmetry groups ofK at x; i.e., the largest subgroup of PGL(3) which leaves Kx invariant as a rational function on P2. We refer to any one of these as a sectional curvature symmetry, or SCS for short. Here is the list.