Journal of Geometry

, Volume 89, Issue 1–2, pp 138–147

Certain Results on K-Contact and (k, μ)-Contact Manifolds

Article

Abstract.

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 E3 or En+1 × Sn (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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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of New HavenWest HavenUSA

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