Turgut Vanlı, Aysel; Ünal, İnan; Avcu, Keziban

In this article, we study a class of normal complex contact metric manifold called a complex Sasakian manifolds. This kind of manifolds have a globally defined complex contact form and normal complex contact structure. We define a complex Sasakian manifold by considering the real case and we present general properties. Also, we obtain some useful curvature relations. Finally, we examine flatness conditions for general curvature tensor B.

AtıfScopus3·OpenAlex2

İncele

Vanli, Aysel Turgut; Unal, Inan

In this paper, we obtain the necessary and sufficient conditions a complex almost contact metric manifold to be normal. In addition, we give some new identities for the Riemann curvature and the Ricci curvatures of normal complex contact metric manifolds. Furthermore, we show that a Ricci semi-symmetric normal complex contact metric manifold is Einstein.

AtıfScopus5

İncele

Vanli, Aysel Turgut; Ünal, Inan; Özdemir, Dilek

In this paper, we study on normal complex contact metric manifold admitting a semi symmetric metric connection. We obtain curvature properties of a normal complex contact metric manifold admitting a semi symmetric metric connection. We also prove that this type of manifold is not conformal flat, concircular flat, and conharmonic flat. Finally, we examine complex Heisenberg group with the semi symmetric metric connection.

AtıfScopus24·WoS25·OpenAlex26

İncele

Turgut Vanli, Aysel; Unal, Inan

IK-normal complex contact metric manifolds have some important properties. There are several applications of this kind of contact manifolds in theoretical physics. In this paper, we studied on H-curvature tensors for IK-normal complex contact metric manifolds. We have shown that there is no IK-normal complex contact metric manifold with constant sectional curvature and an IK-normal complex contact metric manifold is not Ricci semi-symmetric.

AtıfScopus4·WoS2·OpenAlex3

İncele

Vanli, Aysel Turgut; Unal, Inan

Conformal, concircular, quasi-conformal and conharmonic curvature tensors play an important role in Riemannian geometry. In this paper, we study on normal complex contact metric manifolds under flatness conditions of these tensors.

AtıfScopus12·WoS13·OpenAlex19

İncele