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Commun. Korean Math. Soc. 2012; 27(4): 795-808
Printed December 1, 2012
https://doi.org/10.4134/CKMS.2012.27.4.795
Copyright © The Korean Mathematical Society.
On a class of three-dimensional trans-Sasakian manifolds
Uday Chand De and Krishnendu De
Calcutta University, Konnagar High School
The object of the present paper is to study $3$-dimensional trans-Sasakian manifolds with conservative curvature tensor and also $3$-dimensional conformally flat trans-Sasakian manifolds. Next we consider compact connected $\eta$-Einstein $3$-dimensional trans-Sasakian manifolds. Finally, an example of a $3$-dimensional trans-Sasakian manifold is given, which verifies our results.
Keywords: trans-Sasakian manifold, conservative curvature tensor, $\eta$-Einstein manifold
MSC numbers: 53C15, 53C25
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