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

By R. Caddeo, C. Oniciuc, P. Piu. 2003

54 citations recorded by the source corpus.

We consider the biharmonicity condition for maps between Riemann- ian 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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/69e3b4a42399bfe819727d4e1f95267a3781afe4

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

A short survey on biharmonic maps between Riemannian manifolds (2005, methodology): “Using System (4.4), in [ 16 ], R. Caddeo, C. Oniciuc and P. Piu showed that a proper biharmonic curve in H3 is a helix and gave their explicit parametrizations, as shown in the following”
On the biharmonic and harmonic indices of the Hopf map (2004, methodology): “In the presence of nonconstant sectional curvature, a parametric description of all nongeodesic biharmonic curves of the Heisenberg group is given in [6], whereas Inoguchi classified, in [10], the biharmonic Legendre curves and Hopf cylinders on a 3-dimensional Sasakian space form and Sasahara…”