Helix surfaces in Lorentzian Heisenberg group

Abstract

In this work we investigate constant angle surfaces in the Lorentzian Heisenberg group $\htt$. After providing a complete description of the geometry of the ambient space, we perform the full classification of minimal and CMC helix surfaces in $\htt$, giving their explicit parametrizations. In addition, we investigate the constant angle spacelike and timelike surfaces for a Lorentzian metric on the Heisenberg group $H_3$ not treated before in the literature, first showing that such surfaces have constant Gaussian curvature and then obtaining their complete characterization.