Results 21 to 30 of about 249 (140)
Classical and Quantum Gravity, 2000 We show that every Sasakian manifold in dimension $2k+1$ is locally generated by a free real function of $2k$ variables. This function is a Sasakian analogue of the Kähler potential for Kähler geometry. It is also shown that every locally Sasakian-Einstein manifold in $2k+1$ dimensions is generated by a locally Kähler-Einstein manifold in dimension $2k$
Godliński, Michał +2 more
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Submanifolds of a conformal Sasakian manifold
Boletim da Sociedade Paranaense de Matemática, 2020 In the present paper, some results on geometry of conformal Sasakian manifolds and their associated submanifolds are provided. Besides this an example of a three-dimensional conformal Sasakian manifold is constructed for illustration that is not Sasakian manifold.
Esmaiel Abedi, Mohammad Ilmakchi
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Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1993 Let \((M,g)\) be a Riemannian manifold. If \(\xi\) is a Killing vector field of unit length, \(\eta\) is the 1-form dual to \(\xi\) with respect to \(g\) and \(\Phi\) is the tensor field of type \((1,1)\) defined by \(\Phi= \nabla\xi\), \(\xi\) is said to be a Sasakian structure if the two following conditions are fulfilled: \((\nabla_ X \Phi) (Y ...
Boyer, Charles P. +2 more
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Higgs Bundles on Sasakian Manifolds [PDF]
International Mathematics Research Notices, 2017 We extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact Kähler manifolds to compact quasi-regular Sasakian manifolds. A particular consequence is the translation of restrictions on Kähler groups proved using the Donaldson-Corlette-Hitchin-Simpson correspondence to fundamental groups of ...
Biswas, Indranil, Mj, Mahan
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Uniformizations of Compact Sasakian Manifolds
International Mathematics Research Notices, 2023 Abstract We give a criterion for compact Sasakian manifolds to be deformed to Sasakian manifolds, which are locally isomorphic to circle bundles of anti-canonical bundles over Hermitian symmetric spaces as a Sasakian analogue of Simpson’s uniformization results related to variations of Hodge structure and Higgs bundles.
Kasuya, Hisashi, Miyatake, Natsuo
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Three-dimensional trans-Sasakian manifolds and solitons [PDF]
Arab Journal of Mathematical Sciences, 2022 Purpose – The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds.
Sudhakar Kumar Chaubey, Uday Chand De
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A (CHR)3-flat trans-Sasakian manifold
Pracì Mìžnarodnogo Geometričnogo Centru, 2019 In [4] M. Prvanovic considered several curvaturelike tensors defined for Hermitian manifolds. Developing her ideas in [3], we defined in an almost contact Riemannian manifold another new curvaturelike tensor field, which is called a contact ...
Koji Matsumoto
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$m$-quasi-$*$-Einstein contact metric manifolds
Karpatsʹkì Matematičnì Publìkacìï, 2022 The goal of this article is to introduce and study the characterstics of $m$-quasi-$*$-Einstein metric on contact Riemannian manifolds. First, we prove that if a Sasakian manifold admits a gradient $m$-quasi-$*$-Einstein metric, then $M$ is $\eta ...
H.A. Kumara, V. Venkatesha, D.M. Naik
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Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle
Mathematics, 2022 The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle.
Mohammad Nazrul Islam Khan +2 more
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Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection
International Journal of Mathematics and Mathematical Sciences, 2012 We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold.
Bilal Eftal Acet +2 more
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