# On quasi-Sasakian 3-manifolds admitting η-Ricci solitons

TL;DR: In this paper, it was shown that in a quasi-Sasakian 3-manifold admitting Ricci soliton, the structure function is a constant, which is the same as in the present paper.

Abstract: The object of the present paper is to prove that in a quasi-Sasakian\n 3-manifold admitting ?-Ricci soliton, the structure function ? is a\n constant. As a consequence we obtain several important results.

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### "On quasi-Sasakian 3-manifolds admit..." refers background in this paper

...Let M be a (2n + 1)-dimensional connected differentiable manifold endowed with an almost contact metric structure (φ, ξ, η, 1), where φ is a tensor field of type (1, 1), ξ is a vector field, η is a 1-form and 1 is the Riemannian metric on M such that ([4], [5]) φ2X = −X + η(X)ξ, (5)...

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### "On quasi-Sasakian 3-manifolds admit..." refers background in this paper

...Let M be a (2n + 1)-dimensional connected differentiable manifold endowed with an almost contact metric structure (φ, ξ, η, 1), where φ is a tensor field of type (1, 1), ξ is a vector field, η is a 1-form and 1 is the Riemannian metric on M such that ([4], [5]) φ2X = −X + η(X)ξ, (5)...

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### "On quasi-Sasakian 3-manifolds admit..." refers background in this paper

...The notion of quasiSasakian structure was introduced by Blair [6] to unify Sasakian and cosympletic structures....

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