New examples of surfaces in H³ with conformal normal Gauss map

Abstract

In this paper we give some examples of surfaces in H 3 with conformal normal Gauss map with respect to the second conformal structure and prove some global properties.

The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1

“…where g H : M → C ∪ {∞} is exactly the normal Gauss map of x : M → H 3 (cf [8][16] [17]). From this, we also prove the Theorem 4.2.…”

“…From this, the surfaces whose normal Gauss maps are conformal have been found and the translational surfaces with conformal normal Gauss maps locally are given. In [17], the author classified locally the ruled surfaces with conformal normal Gauss maps within the Euclidean ruled surfaces and studied some global properties of the ruled surfaces and translational surfaces with conformal normal Gauss maps.…”