We completely classify Lagrangian H-umbilical Surfaces with λ = 2μ in Complex Lorentzian Plane C1.

The aim of this paper was to obtain Gauss–Bonnet theorems on the Lorentzian Heisenberg group and rigid motions Minkowski plane. At same time, sub-Lorentzian limits Gaussian curvature for surfaces which are C2-smooth in away from characteristic points signed geodesic curves studied. Using a similar method, we also studied corresponding contents

We describe the space of isometric immersions from the Lorentz plane L into the anti-de Sitter 3-space H31, and solve several open problems of this context raised by M. Dajczer and K. Nomizu in 1981. We also obtain from the above result a description of the space of Lorentzian flat tori isometrically immersed in H31 in terms of pairs of closed curves with wave front singularities in the hyperbo...

Lagrangian curves in R entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify Lagrangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R and determ...

Abstract We extend the notion of a Lorentzian pp-wave to that Finsler spacetimes by providing coordinate-independent definition with respect Chern connection; our also includes special case plane wave. This treatment introduces suitable lightlike coordinates, in analogy case, and utilizes anisotropic calculus recently developed one authors. then Penrose’s “plane wave limit” setting spacetimes. ...