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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 28, No. 1, pp. 59-68 (2012)
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Ricci solitons in Lorentzian $\alpha$-Sasakian manifolds

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C. S. Bagewadi and Gurupadavva Ingalahalli

Kuvempu University

**Abstract:** We study Ricci solitons in Lorentzian $\alpha$-Sasakian manifolds. It is shown that a symmetric parallel second order covariant tensor in a Lorentzian $\alpha$-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that if $\mathcal L_Vg+2S$ is parallel, $V$ is a given vector field then $(g,V)$ is Ricci soliton. Further, by virtue of this result Ricci solitons for $(2n+1)$-dimensional Lorentzian $\alpha$-Sasakian manifolds are obtained. Next, Ricci solitons for 3-dimensional Lorentzian $\alpha$-Sasakian manifold whose scalar curvature is constant are obtained.

**Keywords:** Ricci soliton, Lorentzian metric, Sasakian manifold, Einstein

**Classification (MSC2000):** 53C15; 53C20, 53C21, 53C25, 53D10

**Full text of the article:**

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© 2012
FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
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