The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space and ``flat'' spacelike surfacesShyuichi Izumiya and Kentaro Saji
Journal of Singularities
volume 2 (2010), 92-127
Proceedings of Singularities in Aarhus, August 2009
Received: 28 September 2009
Version with corrections: received on December 31, 2010.
Revisions are indicated in red in the pdf. References should be made to the original, published article.
Using the Legendrian dualities between surfaces in pseudo-spheres in Lorentz-Minkowski 4-space, we study various kind of flat surfaces in pseudo-spheres. We consider a surface in the pseudo-sphere and its dual surface. Flatness of a surface is defined by the degeneracy of the dual surface similar to the case for the Gauss map of a flat surface in the Euclidean space. We study singularities of these flat surfaces and dualities of singularities.
Legendrian duality, Horo-spherical geometry, Horo-flat surfaces, Singularities, Lorentz-Minkowski space, Pseudo-spheres
Mathematical Subject Classification:
53A35, 57R45, 53C42
|S. IZUMIYA||K. SAJI|
|Department of Mathematics, Faculty of Science||Department of Mathematics, Faculty of Education|
|Hokkaido University||Gifu University|
|Sapporo 060-0810, Japan||Yanagido 1-1, Gifu, 501-1193, Japan|
|email: email@example.com||email: firstname.lastname@example.org|