(m, ρ)-Quasi-Einstein Metrics in the Frame-Work of K-Contact Manifolds
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The aim of this note is to prove that if a complete K-contact manifold M of dimension (2n + 1) admits a (m, ρ)-quasi-Einstein metric with m ≠ 1, then we prove that f is constant and M becomes compact, Einstein and Sasakian.
KeywordsContact metric manifold K-contact manifold Generalized quasi-Einstein metric (m, ρ)-quasi-Einstein metric
Mathematics Subject Classification (2010)53C24 53C15 53C21
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