Journal of Geometry

, Volume 89, Issue 1, pp 138–147

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

Authors

    • Department of MathematicsUniversity of New Haven
Article

DOI: 10.1007/s00022-008-2004-5

Cite this article as:
Sharma, R. J. geom. (2008) 89: 138. doi:10.1007/s00022-008-2004-5

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).

53C1553C2553A30

Keywords.

K-contact(k, μ)-contactSasakian manifoldsholomorphically planar conformal vector fieldRicci soliton

Copyright information

© Birkhaueser 2008