Contact metric manifolds with <Emphasis Type="Italic">η</Emphasis>-parallel torsion tensor |
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Authors: | Amalendu Ghosh Ramesh Sharma Jong Taek Cho |
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Institution: | (1) Department of Mathematics, Krishnagar Government College, Krishnanagar, 741101, West Bengal, India;(2) Department of Mathematics, University of New Haven, West Haven, CT 06516, USA;(3) Department of Mathematics, Chonnam National University, CNU The Institute of Basic Sciences, Gwangju, 500-757, Korea |
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Abstract: | We show that a non-Sasakian contact metric manifold with η-parallel torsion tensor and sectional curvatures of plane sections containing the Reeb vector field different from 1 at some
point, is a (k, μ)-contact manifold. In particular for the standard contact metric structure of the tangent sphere bundle the torsion tensor
is η-parallel if and only if M is of constant curvature, in which case its associated pseudo-Hermitian structure is CR- integrable. Next we show that if
the metric of a non-Sasakian (k, μ)-contact manifold (M, g) is a gradient Ricci soliton, then (M, g) is locally flat in dimension 3, and locally isometric to E
n+1 × S
n
(4) in higher dimensions.
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Keywords: | η -Parallel torsion tensor (k μ )-Contact manifold Tangent sphere bundle Ricci soliton Sasakian manifold |
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