Codimension one isometric immersions between Lorentz spaces

Abstract

The theorem of Hartman and Nirenberg classifies codimension one isometric immersions between Euclidean spaces as cylinders over plane curves. Corresponding results are given here for Lorentz spaces, which are Euclidean spaces with one negative-definite direction (also known as Minkowski spaces). The pivotal result involves the completeness of the relative nullity foliation of such an immersion. When this foliation carries a nondegenerate metric, results analogous to the Hartman-Nirenberg theorem obtain. Otherwise, a new description, based on particular surfaces in the three-dimensional Lorentz space, is required.