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From a single Sasakian manifold to a family of Sasakian manifolds
Beitrage Zur Algebra Und Geometrie, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gherici Beldjilali +1 more
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Generalized Sasakian space forms and trans-Sasakian manifolds [PDF]
, 2012 Summary: 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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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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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) \(
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Deformation of an LSP-Sasakian Manifold
Acta Universitatis Apulensis, 2014Summary: We shall show LSP Sasakian manifold is invariant under some deformation. Also we shall discuss some properties on LSP Sasakian manifold with the deformation and the behaviour of the Nijenhuis tensor on LSP Sasakian manifold with respect to the same deformation.
Patra, C., Bhattacharyya, A.
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ON SUBMANIFOLDS OF PARA-SASAKIAN MANIFOLDS
JP Journal of Geometry and Topology, 2016Summary: Studying in submanifolds of para-Sasakian manifolds, we obtain that (1) semi-parallel and 2-semi-parallel invariant submanifolds are totally geodesic, (2) necessary and sufficient conditions for the integrability of distributions and (3) some characterizations for submanifolds to be semi-invariant.
Acet, Bilal Eftal +2 more
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1996
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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