The Rough Laplacian and Harmonicity of Hopf Vector Fields

Abstract

Let M be an orientable real hypersurface of a general Kahler manifold \(\bar{M}\). The characteristic vector field ξ of the induced almost contact metric structure (ξ,η, g,ϕ) is also called the Hopf vector field of M. In this paper, we compute the ‘rough’ Laplacian of ξ in terms of the shape operator A and also (as a natural generalization of the contact metric case) in terms of torsion τ = Lξg. Then we give some criteria of harmonicity of ξ. Moreover, we consider hypersurfaces M of contact type and give some criteria for M to admit an H-contact structure.