Results 141 to 150 of about 884 (174)
Hypersurfaces of a Sasakian Manifold [PDF]
Mathematics, 2020 We extend the study of orientable hypersurfaces in a Sasakian manifold initiated by Watanabe. The Reeb vector field ξ of the Sasakian manifold induces a vector field ξ T on the hypersurface, namely the tangential component of ξ to hypersurface, and it also gives a smooth function ρ on the hypersurface, which is the projection ...
Haila Alodan +2 more
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CERTAIN CURVATURE CONDITIONS ON AN LP-SASAKIAN MANIFOLD WITH A COEFFICIENT α
Bulletin of the Korean Mathematical Society, 2009 The object of the present paper is to study certain curvature restriction on an LP-Sasakian manifold with a coefficient α. Among others it is shown that if an LP-Sasakian manifold with a coefficient α is a manifold of constant curvature, then the ...
Uday Chand De, Kadri Arslan
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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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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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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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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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On a type of \(P\)-Sasakian manifold
1992Let \(M\) be a \(P\)-Sasakian manifold in the sense of \textit{I. Satō} [cf. Tensor, New Ser. 30, 219-224 (1976; Zbl 0344.53025)]. Let \(P\) be the Weyl projective curvature tensor of \(M\). It is proved that if \(R(X,Y) \cdot P = 0\), then \(P = 0\). Consequently, \(M\) is of constant negative curvature and \(SP\)-Sasakian.
Tarafdar, Debasish, De, U. C.
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