[Turkmath:5814] METU general seminar, October 27 15:40

[zheltukh at metu.edu.tr]

Dear all,

  You are cordially invited to this week METU Mathematics Department  
general seminar.

  Speaker:  Handan Yıldırım (Istanbul University)

  Title: On Legendrian dual surfaces of a spacelike curve in the  
$3$-dimensional lightcone.

  Abstract: In this talk which is based on the joint work with Kentaro  
Saji given in [1], taking into account
the Legendrian dualities in [2] which are extensions of the Legendrian  
dualities in [3], we first introduce new extended Legendrian dualities  
for the $3$-dimensional pseudo-spheres of various radii in  
Lorentz-Minkowski $4$-space. Secondly, by connecting all of these  
Legendrian dualities continuously, we construct Legendrian dual  
surfaces (lying in these $3$-dimensional pseudo-spheres) of a  
spacelike curve in the $3$-dimensional lightcone. Finally, we  
investigate the singularities of these surfaces and show the dualities  
of the singularities of a certain class of such a surface in the  
$3$-dimensional lightcone.

1. S. Izumiya, "Legendrian dualities and spacelike hypersurfaces in  
the lightcone", Moscow Mathematical Journal,  9 (2009), 325-357.

2. S. Izumiya, H. Yıldırım, "Extensions of the mandala of Legendrian  
dualities for pseudo-spheres in Lorentz-Minkowski space", Topology and  
its Applications, 159 (2012), 509-518.

3. K. Saji, H. Yıldırım, "Legendrian dual surfaces of a spacelike  
curve in the 3-dimensional lightcone",
  Journal of Geometry and Physics, 179 (2022) 104593, 1-21.



  Date: October 27, 2022

  Time: 15:40

  Place: Gündüz Ikeda Seminar Room





   On behalf of research committee,
   Kostyantyn Zheltukhin