Contact metric manifolds whose characteristic vector field is a harmonic vector field
By D. Perrone. 2004
109 citations recorded by the source corpus.
Abstract In this paper, contact metric manifolds whose characteristic vector field ξ is a harmonic vector field are called H -contact manifolds. We show that a (2 n +1)-dimensional contact metric manifold is an H -contact manifold if and only if ξ is an eigenvector of the Ricci operator (J.C. Gonzalez-Davila and L. Vanhecke [J. Geom. 72 (2001) 65–76] proved this result for n =1). Consequently, the class of H -contact manifolds is very large. Moreover, we give some application about the topology of a compact H -contact manifold.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d2acd6242b3f70dd0757443f5857895752347812
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Nullity conditions in paracontact geometry (2012, background): “1) determines the curvature tensor field completely; next, (κ, μ)-spaces provide non-trivial examples of some remarkable classes of contact Riemannian manifolds, like CR-integrable contact metric manifolds ([23]), H-contact manifolds ([22]), harmonic contact metric manifolds ([24]), or contact Riema”
- Certain Contact Metrics as Ricci Almost Solitons (2014, background): “Perrone [17] gives a geometric interpretation of this condition by proving that “A contact metric manifold is an H-contact manifold, that is ξ is a harmonic vector field, if and only if ξ is an eigenvector of the Ricci operator”.”
- The harmonicity of the Reeb vector field on contact metric 3-manifolds (2008, unknown): “By [Perrone 2004] we deduce easily that the characteristic vector field ξ is a harmonic vector field if and only if σ = 0.”
- Geometry of $H$-paracontact metric manifolds (2013, background): “The second author [18] proved that the Reeb vector field ξ of a contact Riemannian manifold is harmonic if and only if ξ is a Ricci eigenvector.”