Twistorial constructions of spacelike surfaces in Lorentzian 4-manifolds
نویسنده
چکیده
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 R 4 1, S 4 1 and H 4 1 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 R 4 1, S 4 1 and H 4 1 those surfaces are explicitly constructed and classified.
منابع مشابه
Contributions to differential geometry of spacelike curves in Lorentzian plane L2
In this work, first the differential equation characterizing position vector of spacelike curve is obtained in Lorentzian plane $mathbb{L}^{2}.$ Then the special curves mentioned above are studied in Lorentzian plane $mathbb{L}%^{2}.$ Finally some characterizations of these special curves are given in $mathbb{L}^{2}.$
متن کاملSpacelike Willmore surfaces in 4-dimensional Lorentzian space forms
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them holds...
متن کاملSpacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b
We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k
متن کاملPolar transform of Spacelike isothermic surfaces in 4-dimensional Lorentzian space forms
The conformal geometry of spacelike surfaces in 4-dimensional Lorentzian space forms has been studied by the authors in a previous paper, where the so-called polar transform was introduced. Here it is shown that this transform preserves spacelike conformal isothermic surfaces. We relate this new transform with the known transforms (Darboux transform and spectral transform) of isothermic surface...
متن کاملTwistorial Harmonic Morphisms with One-dimensional Fibres on Self-dual Four-manifolds
We classify twistorial harmonic morphisms with one-dimensional fibres from self-dual four-manifolds. Along the way, we find two new constructions of
متن کامل