Research Article

Ricci η-parallel trans-Sasakian 3-manifolds

Published in: Quaestiones Mathematicae
Volume 44 , issue 1 , 2021 , pages: 7–15

DOI: 10.2989/16073606.2019.1657980

Author(s): Yan Zhao , P. R. China

Keywords: Primary: 53D15 , Secondary: 53C25 , Primary: 53D15 , Secondary: 53C25

Abstract

In this paper, we present a new characterization for a trans-Sasakian 3-manifold to be proper. More precisely, we prove that if a compact trans-Sasakian 3-manifold has η-parallel Ricci operator, then the manifold is homothetic to a cosymplectic or a Sasakian 3-manifold or is of type (0, β) with ∇β = ξ(β)ξ.

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