Glasnik Matematicki, Vol. 53, No. 1 (2018), 205-220.

η-RICCI SOLITONS IN (ε)-ALMOST PARACONTACT METRIC MANIFOLDS

Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet and Feyza Esra Erdoğan

Department of Mathematics, West University of Timişoara, 300223 Timişoara, România
e-mail: adarablaga@yahoo.com

Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey
e-mail: sperktas@adiyaman.edu.tr

Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey
e-mail: eacet@adiyaman.edu.tr

Department of Elementary Education, Adıyaman University, 02040 Adıyaman, Turkey
e-mail: ferdogan@adiyaman.edu.tr


Abstract.   The object of this paper is to study η -Ricci solitons on ( ε ) -almost paracontact metric manifolds. We investigate η -Ricci solitons in the case when its potential vector field is exactly the characteristic vector field ξ of the ( ε ) -almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and ( ε )-para Sasakian manifolds admitting η-Ricci solitons. Finally we obtain some results for η -Ricci solitons on ( ε )-almost paracontact metric manifolds with a special view towards parallel symmetric (0,2) -tensor fields.

2010 Mathematics Subject Classification.   53C15, 53C25, 53C40, 53C42, 53C50.

Key words and phrases.   ( ε ) -almost paracontact metric manifold, ( ε ) -para Sasakian manifold, Einstein-like manifold, η -Ricci soliton.


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DOI: 10.3336/gm.53.1.14


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