Biharmonic Reeb curves in Sasakian manifolds
Differential Geometry
2010-08-12 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1008.1903,
title = {Biharmonic Reeb curves in Sasakian manifolds},
author = {S. Degla and L. Todjihounde},
journal= {arXiv preprint arXiv:1008.1903},
year = {2010}
}