English

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}
}