Legendrian dual surfaces in hyperbolic 3-space

Kentaro Saji, and Handan Yıldırım. "Legendrian dual surfaces in hyperbolic 3-space." Annales Polonici Mathematici 115.3 (2015): 241-261. <http://eudml.org/doc/280788>.

@article{KentaroSaji2015,
abstract = {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.},
author = {Kentaro Saji, Handan Yıldırım},
journal = {Annales Polonici Mathematici},
keywords = {Lorentz-Minkowski space; Legendrian dualities; hyperbolic 3-space; singularities},
language = {eng},
number = {3},
pages = {241-261},
title = {Legendrian dual surfaces in hyperbolic 3-space},
url = {http://eudml.org/doc/280788},
volume = {115},
year = {2015},
}

TY - JOUR
AU - Kentaro Saji
AU - Handan Yıldırım
TI - Legendrian dual surfaces in hyperbolic 3-space
JO - Annales Polonici Mathematici
PY - 2015
VL - 115
IS - 3
SP - 241
EP - 261
AB - 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.
LA - eng
KW - Lorentz-Minkowski space; Legendrian dualities; hyperbolic 3-space; singularities
UR - http://eudml.org/doc/280788
ER -