Yazar "Cetinkaya, Azime" seçeneğine göre listele

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    Certain results on a type of contact metric manifold
    (Springer Heidelberg, 2015) De, Uday Chand; Yildiz, Ahmet; Cetinkaya, Azime
    Let M be a 3-dimensional almost contact metric manifold satisfying (*) condition. We denote such a manifold by M*. At first we study symmetric and skew-synunetric parallel tensor of type (0, 2) in M*. Next we prove that a non-cosymplectic manifold M* is Ricci semisymmetric if and only if it is Einstein. Also we study locally phi-symmetry and eta-parallel Ricci tensor of M*. Finally, we prove that if a non-cosymplectic M* is Einstein, then the manifold is Sasakian.
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    On some classes of 3-dimensional generalized (?, ?)-contact metric manifolds
    (Tubitak Scientific & Technological Research Council Turkey, 2015) Yildiz, Ahmet; De, Uday Chand; Cetinkaya, Azime
    The object of the present paper is to obtain a necessary and sufficient condition for a 3-dimensional generalized (kappa, mu)-contact metric manifold to be locally phi-symmetric in the sense of Takahashi and the condition is verified by an example. Next we characterize a 3-dimensional generalized (kappa, mu)-contact metric manifold satisfying certain curvature conditions on the concircular curvature tensor. Finally, we construct an example of a generalized (kappa, mu)-contact metric manifold to verify Theorem 1 of our paper.
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    SOME SEMISYMMETRY CONDITIONS ON RIEMANNIAN MANIFOLDS
    (Univ Nis, 2014) Yildiz, Ahmet; Cetinkaya, Azime
    We study a Riemannian manifold M admitting a semisymmetric metric connection (del) over tilde such that the vector field U is a parallel unit vector field with respect to the Levi-Civita connection del. Firstly, we show that ifMis projectively flat with respect to the semisymmetric metric connection (del) over tilde then M is a quasi-Einstein manifold. Also we prove that if R.(P) over tilde = 0 if and only ifMis projectively semisymmetric; if (P) over tilde .R = 0 or R.(P) over tilde-(P) over tilde .R = 0 then Mis conformally flat and quasi-Einstein manifold. Here R, P and (P) over tilde denote Riemannian curvature tensor, the projective curvature tensor of del and the projective curvature tensor of (del) over tilde, respectively.