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On Trans-Sasakian manifolds

On Trans-Sasakian manifolds
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On Invariant Submanifolds of a Nearly Trans-Sasakian Manifold

Arabian Journal for Science and Engineering, 2011
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Sari, R., Vanli, AYSEL
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Trans-Sasakian Manifolds Homothetic to Sasakian Manifolds

Mediterranean Journal of Mathematics, 2015
Let \((M,\varphi,\xi,\eta,g,\alpha,\beta)\) 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, Deshmukh Sharief
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A Note on Compact Trans-Sasakian Manifolds

Mediterranean Journal of Mathematics, 2015
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Sharief Deshmukh, Falleh R Al-Solamy, Deshmukh Sharief   +2 more
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On weakly symmetric generalized trans-sasakian manifold

Commentationes Mathematicae, 2015
In this paper, we have defined the weakly symmetric generalized Trans-Sasakian manifold \(G(WS)_n\) and it has been shown that on such manifold if any two of the vector fields \(\lambda,\gamma,\tau\), defined by equation (0.3) are orthogonal to \(\xi\), then the third will also be orthogonal to \(\xi\). We have also proved that the scalar curvature \(r\
Levejoy S. Das, Ram Nivas, Rupali Agnihotri   +2 more
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Generalized Trans-Sasakian manifolds

Differential Geometry and its Applications, 2023
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Moulay Larbi Sinacer, Gherici Beldjilali, Benaoumeur Bayour, Habib Bouzir   +3 more
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Invariant submanifolds of a trans-Sasakian manifold

Publicationes Mathematicae Debrecen, 2022
An n-dimensional Riemannian manifold M with almost contact metric structure (\(\phi\),\(\xi\),\(\eta\),g) and fundamental 2-form \(\Phi\) is called trans-Sasakian, if \[ (\nabla_ X\Phi)(Y,Z)=(1/2n)[g(x,Y)\eta (Z)- g(X,Z)\eta (Y))\delta \Phi (\xi)+(g(X,\phi Y)\eta (Z)-g(X,\phi Z)\eta (Y))\delta \eta] \] for all vector fields X, Y, Z on M, where \(\delta\
Chinea, D., Perestelo, P. S.
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On semi-invariant submanifolds of a nearly trans-Sasakian manifold admitting a semi-symmetric semi-metric connection

Demonstratio Mathematica, 2013
We define a semi-symmetric semi-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a semi-symmetric semi-metric connection.
Lovejoy S Das, Mobin Ahmad
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Trans-Sasakian manifolds homothetic to Sasakian manifolds

Publicationes Mathematicae Debrecen, 2016
Let \((M,g,\eta,\varphi,\xi)\) 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, De, Uday Chand, Al-Solamy, Falleh   +2 more
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Nullity Condition on Trans-Sasakian 3-Manifolds

Proceedings of the Bulgarian Academy of Sciences, 2022
In this paper, we are concerned with the κ-nullity condition on trans-Sasakian manifolds of dimension three. Such manifolds are classified under an additional assumption that the scalar curvature is invariant along the Reeb flow or a topology restriction.
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