Tohoku Mathematical Journal
2015
December
SECOND SERIES VOL. 67, NO. 4

Tohoku Math. J.
67 (2015), 611-634

Title EXTREMAL LORENTZIAN SURFACES WITH NULL $r$-PLANAR GEODESICS IN SPECE FORMS

Author Kazuyuki Hasegawa and Kouhei Miura

(Received April 15, 2014, revised August 5, 2014)
Abstract. 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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