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Tohoku Mathematical Journal
SECOND SERIES VOL. 67, NO. 4
|Tohoku Math. J.|
67 (2015), 611-634
EXTREMAL LORENTZIAN SURFACES WITH NULL $r$-PLANAR GEODESICS IN SPECE FORMS
Kazuyuki Hasegawa and Kouhei Miura
(Received April 15, 2014, revised August 5, 2014)
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.
Mathematics Subject Classification.
Primary 53C50; Secondary 53C42.
Key words and phrases.
Extremal Lorentzian surfaces, higher fundamental forms, reflector lifts, Boruvka spheres.
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