Timelike minimal surfaces in the three-dimensional Heisenberg group

2022/03/08 by Kiyohara, Hirotaka, Kobayashi, Shimpei
#58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A10 #Secondary 53C42

paper · doi:10.48550/arxiv.2203.03834

Abstract

Timelike surfaces in the three-dimensional Heisenberg group with left invariant semi-Riemannian metric are studied. In particular, non-vertical timelike minimal surfaces are characterized by the non-conformal Lorentz harmonic maps into the de Sitter two phere. On the basis of the characterization, the generalized Weierstrass type representation will be established through the loop group decompositions.

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