Families of minimal surfaces in ℍ² × ℝ foliated by arcs and their Jacobi fields

2019/01/13 by Leonor Ferrer, Ferrer, Leonor, Francisco Martín +5
Mathematics · #49Q05 #49Q10 #53A10 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1901.04066

openalex publication_date 2019/01/13 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

This note provides some new perspectives and calculations regarding an interesting known family of minimal surfaces in ℍ² × ℝ. The surfaces in this family are the catenoids, parabolic catenoids and tall rectangles. Each is foliated by either circles, horocycles or circular arcs in horizontal copies of ℍ². All of these surfaces are well-known, but the emphasis here is on their unifying features and the fact that they lie in a single continuous family. We also initiate a study of the Jacobi operator on the parabolic catenoid, and compute the Jacobi fields associated to deformations to either of the two other types of surfaces in this family.

Related

• Minimal surfaces in ℝ⁴ foliated by conic sections and parabolic rotations of holomorphic null curves in ℂ⁴
• Generalized Riemann minimal surfaces examples in three-dimensional manifolds products
• New complete embedded minimal surfaces in H2xR
• A note on surfaces in \h²×\r
• The Riemann minimal examples