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Open AccessArticle

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

by Yan Zhao 1, Wenjie Wang 2,* and Ximin Liu 2
1
Department of Mathematics, College of Science, Henan University of Technology, Zhengzhou 450001, Henan, China
2
Wenjie Wang, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(11), 246; https://doi.org/10.3390/math6110246
Received: 19 September 2018 / Revised: 3 November 2018 / Accepted: 6 November 2018 / Published: 9 November 2018
(This article belongs to the Special Issue Differential Geometry)
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. View Full-Text
Keywords: trans-Sasakian 3-manifold; Reeb flow symmetry; Ricci operator trans-Sasakian 3-manifold; Reeb flow symmetry; Ricci operator
MDPI and ACS Style

Zhao, Y.; Wang, W.; Liu, X. Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator. Mathematics 2018, 6, 246.

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