Isometric deformations of mixed type surfaces in Lorentz-Minkowski space

Abstract

A connected regular surface in Lorentz-Minkowski 3-space is called a mixed type surface if the spacelike, timelike and lightlike point sets are all non-empty. Lightlike points on mixed type surfaces may be regarded as singular points of the induced metrics. In this paper, we introduce the L-Gauss map around non-degenerate lightlike points, and show the fundamental theorem of surface theory for mixed type surfaces at non-degenerate lightlike points. As an application, we prove that a real analytic mixed type surface admits nontrivial isometric deformations around generic lightlike points.

Behavior of torsion functions of spacelike curves in Lorentz-Minkowski space

“…We introduce a torsion-like invariant called the pseudotorsion function, which yields the fundamental theorem for such spacelike curves (Theorem 3.5, Corollary 3.6). An application of such the fundamental theorem for mixed type surfaces in L 3 can be found in [8].…”