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Article

Hui, Shyamal Kumar ; Chakraborty, Debabrata
$\eta $-Ricci Solitons on $\eta $-Einstein $(LCS)_n$-Manifolds. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 55 (2016), issue 2, pp. 101-109
MSC: 53B30, 53C15, 53C25 | Zbl 1365.53022
Keywords:
$\eta $-Ricci soliton; $\eta $-Einstein manifold; $(LCS)_n$-manifold
Summary:
The object of the present paper is to study $\eta $-Ricci solitons on $\eta $-Einstein $(LCS)_n$-manifolds. It is shown that if $\xi $ is a recurrent torse forming $\eta $-Ricci soliton on an $\eta $-Einstein $(LCS)_n$-manifold then $\xi $ is (i) concurrent and (ii) Killing vector field.
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