0000000000876377
AUTHOR
M. C. Romero-fuster
The horospherical geometry of surfaces in hyperbolic 4-space
We study some geometrical properties associated to the contacts of surfaces with hyperhorospheres inH + 4 (−1). We introduce the concepts of osculating hyperhorospheres, horobinormals, horoasymptotic directions and horospherical points and provide conditions ensuring their existence. We show that totally semiumbilical surfaces have orthogonal horoasymptotic directions.
Graphs of stable maps from closed surfaces to the projective plane
Abstract We describe how to attach a weighted graph to each stable map from closed surfaces to projective plane and prove that any weighted graph with non negatively weighted vertices is the graph of some stable map from a closed surface to the projective plane.