Comparison and rigidity theorems in semi-Riemannian geometry
Comparison and rigidity theorems in semi-Riemannian geometry
The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case correspond to one-sided bounds on the sectional curvatures.Starting from 2-dimensional rigidity results and using an …