EconPapers    
Economics at your fingertips  
 

On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups

Giovanni Calvaruso, Marco Castrillón‐Lopez and Lorenzo Pellegrino

Mathematische Nachrichten, 2025, vol. 298, issue 6, 1922-1942

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.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.12020

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:298:y:2025:i:6:p:1922-1942

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().

 
Page updated 2025-07-02
Handle: RePEc:bla:mathna:v:298:y:2025:i:6:p:1922-1942