Explicit Formulas for Non-Geodesic Biharmonic Curves of the Heisenberg Group

2003/11/13 by R. Caddeo, Renzo Caddeo, C. Oniciuc +6
Mathematics · Physics and Astronomy · #31B30 #58E20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:31B30 #msc:58E20

paper · pdf · doi:10.48550/arxiv.math/0311221

16 pages, 2 figures

arxiv created 2003/11/13 · openalex publication_date 2003/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the biharmonicity condition for maps between Riemannian manifolds (see [BK]), and study the non-geodesic biharmonic curves in the Heisenberg group H₃. First we prove that all of them are helices, and then we obtain explicitly their parametric equations.

Citations

• Harmonic Mappings of Riemannian Manifolds

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