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    Generalized Quasi-Einstein Metrics and Contact Geometry
    (Kyungpook Natl Univ, Dept Mathematics, 2022) Biswas, Gour Gopal; De, Uday Chand; Yildiz, Ahmet
    The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.