Biharmonic Reeb curves in Sasakian manifolds

Details Biharmonic Reeb curves in Sasakian manifolds Biharmonic Reeb curves in Sasakian manifolds

2010-08-11

arxiv.org/abs/1008.1903v1

Mathematics

Differential Geometry

Scientific paper

Sasakian manifolds provide explicit formulae of some Jacobi operators which describe the biharmonic equation of curves in Riemannian manifolds. In this paper we characterize non-geodesic biharmonic curves in Sasakian manifolds which are either tangent or normal to the Reeb vector field. In the three-dimensional case, we prove that such curves are some helixes whose geodesic curvature and geodesic torsion satisfy a given relation.

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