Twistorial construction of spacelike surfaces in Lorentzian 4-manifolds (Q2735666)

The twistor spaces of Lorentzian 4-spaces \(M^4_1\) with natural almost optical structures and induced CR-structures are discussed, especially of the Minkowski space \(R^4_1\), the pseudosphere \(S^4_1\) and the pseudoparabolic space \(H^4_1\). Nonvertical holomorphic curves in the twistor space of \(M^4_1\) project to null-umbilic surfaces and to surfaces with mean curvature of vanishing length in \(M^4_1\). Such surfaces are constructed in \(R^4_1, S^4_1,H^4_1\).NEWLINENEWLINEFor the entire collection see [Zbl 0954.00038].