Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator

Yan Zhao, Wenjie Wang and Ximin Liu
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Yan Zhao: Department of Mathematics, College of Science, Henan University of Technology, Zhengzhou 450001, Henan, China
Wenjie Wang: Wenjie Wang, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China
Ximin Liu: Wenjie Wang, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China

Mathematics, 2018, vol. 6, issue 11, 1-7

Abstract: Let M be a three-dimensional trans-Sasakian manifold of type ( α , β ) . In this paper, we obtain that the Ricci operator of M is invariant along Reeb flow if and only if M is an α -Sasakian manifold, cosymplectic manifold or a space of constant sectional curvature. Applying this, we give a new characterization of proper trans-Sasakian 3-manifolds.

Keywords: trans-Sasakian 3-manifold; Reeb flow symmetry; Ricci operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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