Bulletin of the Belgian Mathematical Society - Simon Stevin

Ricci solitons in almost $f$-cosymplectic manifolds

Xiaomin Chen

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Abstract

In this article we study an almost $f$-cosymplectic manifold admitting a Ricci soliton. We first prove that there do not exist Ricci solitons on an almost cosymplectic $(\kappa,\mu)$-manifold. Further, we consider an almost $f$-cosymplectic manifold admitting a Ricci soliton whose potential vector field is the Reeb vector field and show that a three dimensional almost $f$-cosymplectic is a cosymplectic manifold. Finally we classify a three dimensional $\eta$-Einstein almost $f$-cosymplectic manifold admitting a Ricci soliton..

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 2 (2018), 305-319.

Dates
First available in Project Euclid: 27 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1530065014

Digital Object Identifier
doi:10.36045/bbms/1530065014

Mathematical Reviews number (MathSciNet)
MR3819127

Zentralblatt MATH identifier
1395.53085

Subjects
Primary: 53D15: Almost contact and almost symplectic manifolds 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords
Ricci soliton almost $f$-cosymplectic manifold almost cosymplectic manifold Einstein manifold $(\kappa,\mu)$-manifold

Citation

Chen, Xiaomin. Ricci solitons in almost $f$-cosymplectic manifolds. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 2, 305--319. doi:10.36045/bbms/1530065014. https://projecteuclid.org/euclid.bbms/1530065014


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