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Cubo (Temuco)
On-line version ISSN 0719-0646
Cubo vol.21 no.3 Temuco Dec. 2019
http://dx.doi.org/10.4067/S0719-06462019000300063
Articles
Beta-almost Ricci solitons on Sasakian 3-manifolds
1Department of Pure Mathematics, University of Calcutta, 35, Ballygaunge Circular Road, Kolkata 700019, West Bengal, India. mpradipmajhi@gmail.com.
2Department of Pure Mathematics, University of Calcutta, 35, Ballygaunge Circular Road, Kolkata 700019, West Bengal, India. debabratakar6@gmail.com
In this paper we characterize the Sasakian 3-manifolds admitting β-almost Ricci solitons whose potential vector field is a contact vector field. Among others we prove that a β-almost Ricci soliton whose potential vector field is a contact vector field on a Sasakian 3-manifold is shrinking, Einstein and non-trivial. Moreover, we prove that this type of manifolds are isometric to a sphere of radius √7.
Keywords and Phrases: Ricci soliton; β-almost Ricci soliton; Sasakian 3-manifolds; Einstein
En este artículo caracterizamos las 3-variedades Sasakianas que admiten solitones β-casi Ricci cuyo campo de vectores potencial es un campo de vectores de contacto. Entre otros, probamos que un solitón β-casi Ricci cuyo campo de vectores potencial es un campo de vectores de contacto en una 3-variedad Sasakiana se contrae, es Einstein y no trivial. Más aín, probamos que este tipo de variedades son isométricas a una esfera de radio √7.
Acknowledgement.
The authors are thankful to the referee for his/her valuable suggestions and comments towards the improvement of the paper. The author Debabrata Kar is supported by the Council of Scientific and Industrial Research, India (File no : 09/028(1007)/2017-EMR-1).
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