# On Extended Legendrian Dualities for the Pseudo-Spheres in Lorentz-Minkowski Space

#### Istanbul University

Abstract: In this talk, after one-parameter families of Legendrian dualities in [5] which are the extensions of four Legendrian dualities defined in [4] for the pseudo spheres in Lorentz-Minkowski space are showed, some applications of these extended Legendrian dualities are given, [2,5,6].

References:
[1] V. I. Arnol’d, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differentiable Maps, Vol. I, Birkh ̈auser, 1986.
[2] M. Asayama, S. Izumiya, A. Tamaoki and H. Yıldırım, Slant geometry of spacelike hypersurfaces in Hyperbolic space and de Sitter space, Revista Matem ́atica Iberoamericana 28(2) (2012), 371–400.
[3] D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math., Vol. 509, Springer, 1976.
[4] S. Izumiya, Legendrian dualities and spacelike hypersurfaces in the light-cone, Moscow Mathematical Journal 9 (2009), 325–357.
[5] S. Izumiya and H. Yıldırım, Extensions of the mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space, Topology and its Applications 159 (2012), 509–518.
[6] S. Izumiya and H. Yıldırım, Slant geometry of spacelike hypersurfaces in the lightcone, Journal of the Mathematical Society of Japan 63(3) (2011), 715–752.

Yer : MSGSÜ Bomonti Binası, Fizik Bölümü
Tarih : 9 Ekim 2014 Perşembe, 15:00