A note on contact metric manifolds

Abstract

In this paper, first we obtain several necessary and sufficient conditions for a contact metric manifold to be a K-contact manifold and then it is shown that if the Ricci operator of a complete K-contact manifold satisfies a condition like a Codazzi tensor, then it is necessarily a Sasakian manifold.

Keywords

• contact metric manifolds
• K-contact manifolds
• Killing vector field
• Sasakian manifolds

References

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