Almost contact metric manifolds whose Reeb vector field is a harmonic section

@article{Perrone2013AlmostCM,
  title={Almost contact metric manifolds whose Reeb vector field is a harmonic section},
  author={Domenico Perrone},
  journal={Acta Mathematica Hungarica},
  year={2013},
  volume={138},
  pages={102-126}
}
We investigate almost contact metric manifolds whose Reeb vector field is a harmonic unit vector field, equivalently a harmonic section. We first consider an arbitrary Riemannian manifold and characterize the harmonicity of a unit vector field ξ, when ∇ξ is symmetric, in terms of Ricci curvature. Then, we show that for the class of locally conformal almost cosymplectic manifolds whose Reeb vector field ξ is geodesic, ξ is a harmonic section if and only if it is an eigenvector of the Ricci… CONTINUE READING

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