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On Lorentzian α-Sasakian Manifolds
Yildiz, Ahmet,Murathan, Cengizhan Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.1
The present paper deals with Lorentzian ${\alpha}-Sasakian$ manifolds with conformally flat and quasi conform ally flat curvature tensor. It is shown that in both cases, the manifold is locally isometric with a sphere $S^{2^{n}+1}(c)$. Further it is shown that an Lorentzian ${\alpha}-Sasakian$ manifold with R(X, Y).C = 0 is locally isometric with a sphere $S^{2^{n}+1}(c)$, where c = ${\alpha}^2$.
On Semiparallel and Weyl-semiparallel Hypersurfaces of Kaehler Manifolds
Ozgur, Cihan,Murathan, Cengizhan,Arslan, Kadri Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.1
We study on semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds. We prove that a (2n + 1)-dimensional Sasakian hypersurface M of a (2n+2)-dimensional Kaehler manifold $\widetilde{M}^{2n+2}$ is semiparallel if and only if it is totally umbilical with unit mean curvature, if dimM = 3 and $\widetilde{M}^4$ is a Calabi-Yau manifold, then $\widetilde{M}$ is flat at each point of M. We also prove that such a hypersurface M is Weyl-semiparallel if and only if it is either an ${\eta}$-Einstein manifold or semiparallel. We also investigate the extended classes of semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds.
ON SLANT RIEMANNIAN SUBMERSIONS FOR COSYMPLECTIC MANIFOLDS
Erken, Irem Kupeli,Murathan, Cengizhan Korean Mathematical Society 2014 대한수학회보 Vol.51 No.6
In this paper, we introduce slant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We obtain some results on slant Riemannian submersions of a cosymplectic manifold. We also give examples and inequalities between the scalar curvature and squared mean curvature of fibres of such slant submersions in the cases where the characteristic vector field is vertical or horizontal.
A Class of Lorentzian α-Sasakian Manifolds
Yildiz, Ahmet,Turan, Mine,Murathan, Cengizhan Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.4
In this study we consider ${\varphi}$-conformally flat, ${\varphi}$-conharmonically flat, ${\varphi}$-projectively at and ${\varphi}$-concircularly flat Lorentzian ${\alpha}$-Sasakian manifolds. In all cases, we get the manifold will be an ${\eta}$-Einstein manifold.
PSEUDO SYMMETRIC AND PSEUDO RICCI SYMMETRIC WARPED PRODUCT MANIFOLDS
De, Uday Chand,Murathan, Cengizhan,Ozgur, Cihan Korean Mathematical Society 2010 대한수학회논문집 Vol.25 No.4
We study pseudo symmetric (briefly $(PS)_n$) and pseudo Ricci symmetric (briefly $(PRS)_n$) warped product manifolds $M{\times}_FN$. If M is $(PS)_n$, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is $(PRS)_n$, then we show that (i) N is Ricci symmetric and (ii) M is $(PRS)_n$ if and only if the tensor T defined by (2.6) satisfies a certain condition.
On slant Riemannian submersions for cosymplectic manifolds
Irem Kupeli Erken,Cengizhan Murathan 대한수학회 2014 대한수학회보 Vol.51 No.6
In this paper, we introduce slant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We obtain some results on slant Riemannian submersions of a cosymplectic manifold. We also give examples and inequalities between the scalar curvature and squared mean curvature of fibres of such slant submersions in the cases where the characteristic vector field is vertical or horizontal.
CONTACT CR-WARPED PRODUCT SUBMANIFOLDS IN KENMOTSU SPACE FORMS
ARSLAN, KADRI,EZENTAS, RIDVAN,MIHAl, ION,MURATHAN, CENGIZHAN Korean Mathematical Society 2005 대한수학회지 Vol.42 No.5
Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.
Tensor product surfaces with pointwise 1-type Gauss map
Kadri Arslan,Betul Bulca,Bengu Kilic,Young Ho Kim,Cengizhan Murathan,Gunay Ozturk 대한수학회 2011 대한수학회보 Vol.48 No.3
Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle c_1 centered at origin with an Euclidean planar curve c_2 has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle c_1 centered at origin with an Euclidean planar curve c_2 to have pointwise 1-type Gauss map.
TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP
Arslan, Kadri,Bulca, Betul,Kilic, Bengu,Kim, Young-Ho,Murathan, Cengizhan,Ozturk, Gunay Korean Mathematical Society 2011 대한수학회보 Vol.48 No.3
Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ to have pointwise 1-type Gauss map.