Vertically invariant minimal surfaces in unimodular semidirect products

2023/07/27 by David Moya, Moya, David
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2307.14716

openalex publication_date 2023/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

A surface in a three-dimensional metric Lie group G is said invariant if it is invariant with respect to a one-dimensional subgroup Γ of the isometry group of G. Is this work we focus on unimodular metric Lie groups G that can be written as a semidirect product of the form ℝ²\rtimes_A ℝ for certain matrix A∈ M₂(ℝ) and study the minimal surfaces which are invariant under the group Γ generated by left translations by elements in the vertical axis \0\\rtimesℝ. We will call these surfaces vertically invariant. In particular, we describe new examples of minimal surfaces in \widetildeE(2) which are vertically invariant.

Related

• The geometry of stable minimal surfaces in metric Lie groups
• The index of symmetry of three-dimensional Lie groups with a\n left-invariant metric
• Constructions of helicoidal minimal surfaces and minimal annuli in \widetildeE(2)
• Isometric immersions into three-dimensional unimodular metric Lie groups
• Ruled Surfaces in Three Dimensional Lie Groups