A CLASSIFICATION OF (κ, μ)-CONTACT METRIC MANIFOLDS

Yildiz, Ahmet;De, Uday Chand

• Published : 2012.04.30
• 25 5

Abstract

In this paper we study $h$-projectively semisymmetric, ${\phi}$-pro-jectively semisymmetric, $h$-Weyl semisymmetric and ${\phi}$-Weyl semisym- metric non-Sasakian ($k$, ${\mu}$)-contact metric manifolds. In all the cases the manifold becomes an ${\eta}$-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian ($k$, ${\mu}$)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N($k$)-contact metric manifold.

Keywords

semisymmetric spaces;($k$, ${\mu}$)-contact metric manifolds;non-Sasakian manifolds;${\eta}$-Einstein manifolds;$h$-projectively semisymmetric;${\phi}$-projectively semisymmetric;$h$-Weyl semisymmetric;${\phi}$-Weyl semisymmetric

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1. CERTAIN SEMISYMMETRY PROPERTIES OF (𝜅, 𝜇)-CONTACT METRIC MANIFOLDS vol.53, pp.4, 2016, https://doi.org/10.4134/BKMS.b150638
2. ϕ-semisymmetric generalized Sasakian space-forms vol.21, pp.2, 2015, https://doi.org/10.1016/j.ajmsc.2015.01.002
3. ON GENERALIZED QUASI-CONFORMAL N(k, μ)-MANIFOLDS vol.31, pp.1, 2016, https://doi.org/10.4134/CKMS.2016.31.1.163