The Structure of Some Classes of Contact Metric Manifolds

SUT Journal of Mathematics

The object of this paper is to study K-contact manifolds with quasiconformal curvature tensor. We characterised K-contact manifolds satisfying certain curvature conditions on the quasi-conformal curvature tensor.

The question of whether a Sasakian metric can admit an additional compatible ($K$)contact structure is addressed. In the complete case if the second structure is also assumed Sasakian, works of Tachibana-Yu and Tanno show that the manifold must be 3-Sasakian or an odd dimensional sphere with constant curvature. Some extensions of this result are obtained, mainly in dimensions 3 and 5.

Journal of Geometry, 2008

Inspired by a result of Boyer and Galicki, we prove that a complete K-contact gradient soliton is compact Einstein and Sasakian. For the nongradient case we show that the soliton vector field is a Jacobi vector field along the geodesics of the Reeb vector field. Next we show that among all complete and simply connected K-contact manifolds only the unit sphere admits a non-Killing holomorphically planar conformal vector field (HP CV ). Finally we show that, if a (k, μ)-contact manifold admits a non-zero HP CV , then it is either Sasakian or locally isometric to E 3 or E n+1 × S n (4).

2011

We study the Riemann curvature tensor of (\kappa,\mu,\nu)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by D_a-homothetic deformations. This prompts the definition and study of generalized (\kappa,\mu,\nu)-space forms and of the necessary and sufficient conditions for them to be conformally flat.

2011

We study the Riemann curvature tensor of (\kappa,\mu,\nu)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by D_a-homothetic deformations. This prompts the definition and study of generalized (\kappa,\mu,\nu)-space forms and of the necessary and sufficient conditions for them to be conformally flat.

Journal of Mountain Research

We study of complex sasakian manifold which is a type of normal complex contact metric manifold and study of complex -Einstein sasakian manifold [Vanli and Unal, 2017]. Inan Unal and A. Turgut Vanli obtained curvature properties of complex Sasakian manifold [Vanli and Unal, 2019]. We define some relations between curvature tensors of complex Sasakian manifold and obtained some useful results.

2015

We study the Riemann curvature tensor of (κ, µ, ν)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by Da-homothetic deformations. This prompts the definition and study of generalized (κ, µ, ν)-space forms and of the necessary and sufficient conditions for them to be conformally flat.Ministerio de Educación y CienciaFondo Europeo de Desarrollo RegionalPlan Andaluz de Investigación (Junta de Andalucía

SUT Journal of Mathematics

We classify N (k)-contact metric manifolds satisfying the conditions Z(ξ, X) • C 0 = 0, C 0 (ξ, X) • Z = 0 and C e (ξ, X) • Z = 0, where Z, C 0 and C e denote the concircular curvature tensor, the contact conformal curvature tensor and the extended contact conformal curvature tensor, respectively.

Tohoku Mathematical Journal, 1979

Tamkang Journal of …, 2008

Abstract. We prove that a (k,µ)-manifold with vanishing Endo curvature tensor is a Sasakian manifold. We find a necessary and sufficient condition for a non-Sasakian (k,µ)-manifold whose Endo curvature tensor Bes satisfies Bes (ξ, X ) · S = 0, where S is the Ricci tensor. Using ...