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$n$-Sasakian manifoldsWe define a new class of manifolds called $n$-Sasakian manifolds that enjoy remarkable geometric properties. We furnish examples of such manifolds and make links to the study of isoparametric hypersurfaces. We demonstrate that these examples carry Einstein metrics.
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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, Deshmukh Sharief
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3-Quasi-Sasakian manifolds [PDF]
Annals of Global Analysis and Geometry, 2007 In the present paper we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one.
Antonio De Nicola +2 more
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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.
Ahmed Mohammed Cherif +1 more
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Sasakian statistical manifolds
Journal of Geometry and Physics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hitoshi Furuhata +2 more
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On the J-flow in Sasakian manifolds [PDF]
Annali Di Matematica Pura Ed Applicata, 2015 15 ...
Luigi Vezzoni +2 more
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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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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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