Tohoku Mathematical Journal
2025
December
SECOND SERIES VOL. 77, NO. 4

Tohoku Math. J.
77 (2025), 553-581

Title MINIMAL NULL SCROLLS IN THE THREE-DIMENSIONAL HEISENBERG GROUP

Author Hirotaka Kiyohara

(Received August 21, 2023, revised February 5, 2024)
Abstract. In the three-dimensional Heisenberg group equipped with a certain left invariant Lorentzian metric, timelike minimal surfaces which have the Abresch-Rosenberg differentials with vanishing multiplication of the coefficient function and its para-complex conjugate are characterized as the surfaces defined by the multiplication of null curves and affine null lines. Moreover, the constructions of these surfaces with prescribed curvatures of null curves or prescribed null lines are given.

Mathematics Subject Classification. Primary 53A10; Secondary 53A35, 53C42.
Key words and phrases. Surfaces, minimal surfaces, Heisenberg group, timelike surfaces, null scrolls.

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