Spacelike Parallels and Evolutes in Minkowski pseudospheres
Preprint Series # 767 Izumiya, Shyuichi and Takahashi, Masatomo Spacelike Parallels and Evolutes in Minkowski pseudospheres. (2006); AbstractWe consider extrinsic differential geometry on spacelike hypersurfaces in Minkowski pseudospheres (hyperbolic space,
de Sitter space and the lightcone).
In the previous paper we have shown a basic Legendrian duality theorem between pseudospheres.
We define the spacelike parallels by using the basic Legendrian duality theorem. This definition unifies the notions of parallels of
spacelike hypersurfaces in
pseudospheres.
We also define the evolute as the locus of singularities of the
spacelike parallels.
These notions are investigated as applications of Lagrangian
or Legendrian singularity theory.
We consider geometric properties of nonsingular spacelike hypersurfaces
corresponding to singularities of spacelike parallels or evolutes.
Item Type:  Preprint 

Additional Information:  50 

Uncontrolled Keywords:  spacelike parallels, evolutes, caustics, Lagrangian singularities, Legendrian singularities 

Subjects:  53xx DIFFERENTIAL GEOMETRY 

ID Code:  1259 

