Biharmonic Curves in 3-dimensional Hyperbolic Heisenberg Group

Details Biharmonic Curves in 3-dimensional Hyperbolic Heisenberg Group Biharmonic Curves in 3-dimensional Hyperbolic Heisenberg Group

2011-03-03

arxiv.org/abs/1103.0684v1

Mathematics

Differential Geometry

Scientific paper

In this paper we study the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group. We prove that all of the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group are helices. Moreover, we obtain explicit parametric equations for non-geodesic non-null biharmonic curves and non-geodesic spacelike horizontal biharmonic curves in 3-dimensional hyperbolic Heisenberg group, respectively. We also show that there do not exist non-geodesic timelike horizontal biharmonic curves in 3-dimensional hyperbolic Heisenberg group.

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