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A Lorentzian surface in a four-dimensional manifold of neutral signature and its reflector lift. (English) Zbl 1264.53058

Summary: A Lorentzian surface in a four-dimensional manifold of neutral signature is called super-extremal if its reflector lift is horizontal. We give an elementary proof of a rigidity theorem for super-extremal surfaces in the space of constant curvature and neutral signature. As corollary, a characterization of the immersion of the Veronese type is given.

MSC:

53C40 Global submanifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C24 Rigidity results
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