Ricci η-parallel trans-Sasakian 3-manifolds

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 =...

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Bibliographic Details
Published in:Quaestiones mathematicae 2021-01, Vol.44 (1), p.7-15
Main Author: Zhao, Yan
Format: Article
Language:English
Subjects:
Manifolds
Primary: 53D15
Secondary: 53C25
Trans-Sasakian 3-manifold
η-parallel Ricci operator
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Summary: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.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2019.1657980