Semi-Riemannian hypersurfaces in $\mathbb{L}^{n+1}$ with a totally geodesic foliation of codimension one

TL;DR

This paper classifies certain hypersurfaces in Minkowski space that have a special geometric structure, showing they are either ruled, partial tubes, or contain strips, with specific results for embedded cases.

Contribution

It provides a complete classification of semi-Riemannian hypersurfaces with a totally geodesic foliation of codimension one in Minkowski space, including embedded cases.

Findings

Hypersurfaces are either ruled, partial tubes, or contain strips.

Embedded hypersurfaces are partial tubes over a curve.

Classification applies to hypersurfaces with complete leaves of the foliation.

Abstract

We classify hypersurfaces of the Minkowski space $\L^{n+1}$ that carry a totally geodesic foliation with complete leaves of codimension one. We prove that such a hypersurface is ruled, or a partial tube over a curve or contains a two or three dimensional strip. Moreover, if the hypersurface is embedded then it is a partial tube over a curve.