1. Lightlike flat geometry of spacelike submanifolds in Lorentz-Minkowski space
- Author
-
Izumiya, Shyuichi and Kasedou, Masaki
- Subjects
lightcone pedal hypersurface ,Lagrangian/Legendrian singularities ,canal spacelike submanifold ,Lorentz-Minkowski space ,lightcone Gauss maps - Abstract
In this paper, we investigate differential geometry on spacelike submanifolds in Lorentz-Minkowski space from the viewpoint of contact with lightlike hyperplanes. It is called the lightlike flat geometry which has been well established for the codimension-two case. In order to develop the theory for the general codimension-case, we introduce the notion of codimension-two spacelike canal submanifolds which is a main tool in this paper. We apply the theory of Lagrangian/Legendrian singularities to codimension-two spacelike canal submanifolds and obtain the relation with the previous results on the codimension-two case.
- Published
- 2014