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ON Φ-RECURRENT (k, μ)-CONTACT METRIC MANIFOLDS

  • Published : 2008.11.30

Abstract

In this paper we prove that a $\phi$-recurrent (k, $\mu$)-contact metric manifold is an $\eta$-Einstein manifold with constant coefficients. Next, we prove that a three-dimensional locally $\phi$-recurrent (k, $\mu$)-contact metric manifold is the space of constant curvature. The existence of $\phi$-recurrent (k, $\mu$)-manifold is proved by a non-trivial example.

Keywords

(k, $\mu$)-contact metric manifolds;$\eta$-Einstein manifold;$\phi$-recurrent (k, $\mu$)-contact metric manifolds

References

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Cited by

  1. On ϕ-quasiconformally symmetric (κ,μ)-contact manifolds vol.31, pp.4, 2010, https://doi.org/10.1134/S1995080210040086
  2. CERTAIN SEMISYMMETRY PROPERTIES OF (𝜅, 𝜇)-CONTACT METRIC MANIFOLDS vol.53, pp.4, 2016, https://doi.org/10.4134/BKMS.b150638