0000000000739898
AUTHOR
Donghe Pei
THE HOROSPHERICAL GEOMETRY OF SUBMANIFOLDS IN HYPERBOLIC SPACE
Some geometrical properties associated to the contact of submanifolds with hyperhorospheres in hyperbolic -space are studied as an application of the theory of Legendrian singularities.
Umbilicity of space-like submanifolds of Minkowski space
We study some properties of space-like submanifolds in Minkowski n-space, whose points are all umbilic with respect to some normal field. As a consequence of these and some results contained in a paper by Asperti and Dajczer, we obtain that being ν-umbilic with respect to a parallel light-like normal field implies conformal flatness for submanifolds of dimension n − 2 ≥ 3. In the case of surfaces, we relate the umbilicity condition to that of total semi-umbilicity (degeneracy of the curvature ellipse at every point). Moreover, if the considered normal field is parallel, we show that it is everywhere time-like, space-like or light-like if and only if the surface is included in a hyperbolic 3…
Singularities of lightlike hypersurfaces in Minkowski four-space
We classify singularities of lightlike hypersurfaces in Minkowski 4-space via the contact invariants for the corresponding spacelike surfaces and lightcones.