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Trans-Sasakian Manifolds Homothetic to Sasakian Manifolds
Mediterranean Journal of Mathematics, 2015Let \((M,\varphi,\xi,\eta,g,\alpha,\beta)\) be a 3-dimensional compact simply connected trans-Sasakian manifold. It is proved that such a manifold is homothetic to a Sasakian manifold if and only if the functions \(\alpha\) and \(\beta\) satisfy one of the following Poisson equations: 1) \(\Delta\alpha= \beta\); 2) \(\Delta\alpha= \alpha^2\beta\); 3) \(
Sharief Deshmukh
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Trans-Sasakian manifolds homothetic to Sasakian manifolds
Publicationes Mathematicae Debrecen, 2016Let \((M,g,\eta,\varphi,\xi)\) be a \((2n+1)\)-dimensional almost contact metric manifold, where \(g\) is a Riemannian metric, \(\eta\) is a smooth 1-form, \(\xi\) is the Reeb vector field and \(\varphi\) is \((1, 1)\)-tensor field. If there are smooth functions \((\alpha,\beta)\) satisfying \((\nabla \varphi)(X,Y) =\alpha\, (g(X,Y)\xi - \eta(Y)X ...
Desmukh, Sharief +2 more
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Generalized weakly symmetric Sasakian manifolds
2023Summary: In this parer, we give a necessary condition for Sasakian manifolds to be generalized weakly symmetric. We prove the odd-dimensional spheres are the only generalized weakly symmetric Sasakian manifolds. Then, we show that generalized weakly Ricci-symmetric Sasakian manifolds are Einstein.
Pirhadi, Vahid +2 more
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Generalized Trans-Sasakian manifolds
Differential Geometry and its Applications, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Moulay Larbi Sinacer +3 more
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From a single Sasakian manifold to a family of Sasakian manifolds
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gherici Beldjilali +2 more
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2011
Summary: The present paper deals with certain curvature conditions on the projective curvature tensor.
Taleshian, A., Asghari, N.
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Summary: The present paper deals with certain curvature conditions on the projective curvature tensor.
Taleshian, A., Asghari, N.
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2002
In this chapter we will give more of a survey of 3-Sasakian manifolds and only a few proofs. A more thorough treatment is given in the book by Boyer and Galicki [2008, Chapter 13].
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In this chapter we will give more of a survey of 3-Sasakian manifolds and only a few proofs. A more thorough treatment is given in the book by Boyer and Galicki [2008, Chapter 13].
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2012
Let \(\Sigma=(\phi,\xi,\eta, g)\) be a \(P\)-Sasakian structure on a Riemannian manifold \(M\). In this paper, the authors study \(P\)-Sasakian manifolds for which the condition \((*)\;R(\xi,Y)\cdot C=0\) is satisfied, where \(R(X,Y)\) is considered as a derivation of the tensor algebra at each point of \(M\) for tangent vectors \(X\) and \(Y\).
Tarafdar, M., Mayra, A.
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Let \(\Sigma=(\phi,\xi,\eta, g)\) be a \(P\)-Sasakian structure on a Riemannian manifold \(M\). In this paper, the authors study \(P\)-Sasakian manifolds for which the condition \((*)\;R(\xi,Y)\cdot C=0\) is satisfied, where \(R(X,Y)\) is considered as a derivation of the tensor algebra at each point of \(M\) for tangent vectors \(X\) and \(Y\).
Tarafdar, M., Mayra, A.
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Generalized Sasakian space forms and trans-Sasakian manifolds
2012Summary: We study generalized Sasakian space forms and trans-Sasakian manifolds. We present results on generalized recurrent, generalized \(\phi\)-recurrent, \(\phi\)-concircular and \(\phi\)-conharmonically recurrent trans-Sasakian manifolds and generalized Sasakian space forms.
Somashekhara, G., Nagaraja, H. G.
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