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Extremal Lorentzian surfaces with null \(r\)-planar geodesics in space forms. (English) Zbl 1334.53057
Summary: We show a congruence theorem for oriented Lorentzian surfaces with horizontal reflector lifts in pseudo-Riemannian space forms of neutral signature. As a corollary, a characterization theorem is obtained for the Lorentzian Boruvka spheres, that is, a full real analytic null \(r\)-planar geodesic immersion with vanishing mean curvature vector field is locally congruent to the Lorentzian Boruvka sphere in a \(2r\)-dimensional space form of neutral signature.

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
Full Text: DOI Euclid
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