Twistorial constructions of spacelike surfaces in Lorentzian 4-manifolds

الأصل · EN

We investigate the twistor space and the Grassmannian fibre bundle of a Lorentzian 4-space with natural almost optical structures and its induced CR-structures. The twistor spaces of the Lorentzian space forms ⁴₁, S⁴₁ and H⁴₁ are explicitly discussed. The given twistor construction is applied to surface theory in Lorentzian 4-spaces. Immersed spacelike surfaces in a Lorentzian 4-space with special geometric properties like semi-umbilic surfaces and surfaces that have mean curvature of vanishing lengths correspond to holomorphic curves in the Lorentzian twistor space. For the Lorentzian space forms ⁴₁, S⁴₁ and H⁴₁ those surfaces are explicitly constructed and classified.