In this paper we discuss a Weierstrass type representation for minimal surfaces in the3-dimensional Heisenberg group and in the 4-dimensional Damek–Ricci spaces, endowed with left invariant Riemannian or Lorentzian metrics. For the case of spacelike surfaces we employ the complex analysis, and for timelike surfaces our approach makes use of the paracomplex analysis. Then, we exhibit various examples of spacelike and timelike minimal surfaces in these spaces.

Minimal surfaces in Lorentzian Heisenberg group and Damek–Ricci spaces via the Weierstrass representation

MERCURI, FRANCESCO;ONNIS, IRENE IGNAZIA
2017-01-01

Abstract

In this paper we discuss a Weierstrass type representation for minimal surfaces in the3-dimensional Heisenberg group and in the 4-dimensional Damek–Ricci spaces, endowed with left invariant Riemannian or Lorentzian metrics. For the case of spacelike surfaces we employ the complex analysis, and for timelike surfaces our approach makes use of the paracomplex analysis. Then, we exhibit various examples of spacelike and timelike minimal surfaces in these spaces.
2017
Lorentzian Damek–Ricci spaces; Lorentzian Heisenberg group; minimal surfaces; Weierstrass representation; mathematical physics; physics and astronomy (all); geometry and topology
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/263752
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