Certain Results on K-Contact and (k, μ)-Contact Manifolds
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Inspired by a result of Boyer and Galicki, we prove that a complete K-contact gradient soliton is compact Einstein and Sasakian. For the non-gradient case we show that the soliton vector field is a Jacobi vector field along the geodesics of the Reeb vector field. Next we show that among all complete and simply connected K-contact manifolds only the unit sphere admits a non-Killing holomorphically planar conformal vector field (HPCV). Finally we show that, if a (k, μ)-contact manifold admits a non-zero HPCV, then it is either Sasakian or locally isometric to E 3 or E n+1 × S n (4).
Mathematics Subject Classification (2000).53C15 53C25 53A30
Keywords.K-contact (k, μ)-contact Sasakian manifolds holomorphically planar conformal vector field Ricci soliton
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