Spacelike Parallels and Evolutes in Minkowski pseudo-spheres
Preprint Series # 767
Izumiya, Shyuichi and Takahashi, Masatomo Spacelike Parallels and Evolutes in Minkowski pseudo-spheres. (2006);
We consider extrinsic differential geometry on spacelike hypersurfaces in Minkowski pseudo-spheres (hyperbolic space,
de Sitter space and the lightcone).
In the previous paper we have shown a basic Legendrian duality theorem between pseudo-spheres.
We define the spacelike parallels by using the basic Legendrian duality theorem. This definition unifies the notions of parallels of
spacelike hypersurfaces in
We also define the evolute as the locus of singularities of the
These notions are investigated as applications of Lagrangian
or Legendrian singularity theory.
We consider geometric properties of non-singular spacelike hypersurfaces
corresponding to singularities of spacelike parallels or evolutes.
|Uncontrolled Keywords:||spacelike parallels, evolutes, caustics, Lagrangian singularities, Legendrian singularities|
|Subjects:||53-xx DIFFERENTIAL GEOMETRY|