Anti de Sitter horospherical flat timelike surfaces

Abstract

In this paper, we investigate a special timelike surfaces in Anti de Sitter 3-space. We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of Anti de Sitter horocycle. We give a generic classification of singularities and study the geometric properties of such surfaces from the viewpoint of Legendrian singularity theory.

Some Special Associated Curves of Non-degenerate Curve in Anti de Sitter 3-Space

“…where the geodesic torsion of γ is given by τ g (s) = δ1 det(γ(s),γ (s),γ (s),γ We will give the following definitions in [1,2] and also they are valid for S 3 2 .…”

“…In this section, we give the basic theory of local differential geometry of non-degenerate curves in de Sitter 3-space with index 2 and Anti de Sitter 3-space. For more detail and background about these spaces, see [2,10].…”

Singularities of lightcone pedals of spacelike curves in Lorentz-Minkowski 3-space

“…On the other hand, singularity theory tools are useful in the investigation of geometric properties of submanifolds immersed in different ambient spaces, from both the local and global viewpoint [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The natural connection between geometry and singularities relies on the basic fact that the contacts of a submanifold with the models (invariant under the action of a suitable transformation group) of the ambient space can be described by means of the analysis of the singularities of appropriate families of contact functions, or equivalently, of their associated Lagrangian and/or Legendrian maps.…”