Year: 2025
Type: article
Abstract: This paper has manifold purposes. We first introduce a description of the Gauss map for submanifolds (both spacelike and timelike) of a Lorentzian ambient space and relate the conformality of the Gauss map of a surface to total umbilicity and minimality. We then focus on surfaces of the three‐dimensional Heisenberg group, equipped with any of its left‐invariant Lorentzian metrics. We prove that with the obvious exception of the flat case, no totally umbilical surfaces occur. On the other hand, we determine and explicitly describe several examples of minimal and constant mean curvature (CMC) surfaces.
Source: Mathematische Nachrichten
DOI: 10.1002/mana.12020
Authors: Giovanni Calvaruso, Marco Castrillón‐Lopez, Lorenzo Pellegrino
Institutions: University of Salento, Universidad Complutense de Madrid
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,460
OpenAlex ID: W4410521247