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On the geometry of Lorentzian Sasakian manifolds

Bu tezde Lorentzian Sasakian manifoldlarını, bu manifoldların eğrilik tensörlerini ve pseudoparalel altmanifoldlarını araştırdık. Bu tez beş bölümden oluşmaktadır.
Altay, Beyda Nur
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On Trans-Sasakian manifolds

On Trans-Sasakian manifolds
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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 a type of trans-Sasakian manifolds

, 2017
Summary: The object of the present paper is to study \(3\)-dimensional trans-Sasakian manifolds admitting a \(W_2\)-curvature tensor. Trans-Sasakian manifolds satisfying the curvature condition \(S(X,\xi). R = 0\) is also considered.
De, Krishnendu
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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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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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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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