Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 6
On nearly Kenmotsu manifolds
- Pages
- 1040–1047
- DOI
- —
Abstract
We prove that on a nearly Kenmotsu manifold a second-order symmetric closed recurrent tensor is a multiple of the associated metric tensor. We then find the necessary condition under which a vector field on a nearly Kenmotsu manifold will be a strict contact or Killing vector field. Finally, we prove that every f-recurrent nearly Kenmotsu manifold is an Einstein manifold and every locally f-recurrent nearly Kenmotsu manifold is a manifold of constant curvature -1 .
Özet
We prove that on a nearly Kenmotsu manifold a second-order symmetric closed recurrent tensor is a multiple of the associated metric tensor. We then find the necessary condition under which a vector field on a nearly Kenmotsu manifold will be a strict contact or Killing vector field. Finally, we prove that every f-recurrent nearly Kenmotsu manifold is an Einstein manifold and every locally f-recurrent nearly Kenmotsu manifold is a manifold of constant curvature -1 .