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arXiv · 2511.06932

Helix surfaces in Lorentzian Heisenberg group

Lorenzo Pellegrino
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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.

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Lorenzo Pellegrino. 2025-11-10. Helix surfaces in Lorentzian Heisenberg group. https://arxiv.org/abs/2511.06932

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