We consider surfaces in hyperbolic 3-space and their duals. We study flat dual surfaces in hyperbolic 3-space by using extended Legendrian dualities between pseudo-hyperspheres in Lorentz-Minkowski 4-space. We define the flatness of a surface in hyperbolic 3-space by the degeneracy of its dual, which is similar to the case of the Gauss map of a surface in Euclidean 3-space. Such surfaces are a kind of ruled surfaces. Moreover, we investigate the singularities of these surfaces and the dualities of the singularities.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-4,
author = {Kentaro Saji and Handan Y\i ld\i r\i m},
title = {Legendrian dual surfaces in hyperbolic 3-space},
journal = {Annales Polonici Mathematici},
volume = {113},
year = {2015},
pages = {241-261},
zbl = {1338.53022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-4}
}
Kentaro Saji; Handan Yıldırım. Legendrian dual surfaces in hyperbolic 3-space. Annales Polonici Mathematici, Tome 113 (2015) pp. 241-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-4/