Geometric structures associated with a contact metric $(\kappa ,\mu )$-space

Abstract

We prove that any contact metric $(\kappa ,\mu )$-space $(M,\xi ,\varphi ,\eta ,g)$ admits a canonical paracontact metric structure which is compatible with the contact form $\eta$. We study such canonical paracontact structure, proving that it verifies a nullity condition and induces on the underlying contact manifold $(M,\eta )$ a sequence of compatible contact and paracontact metric structures verifying nullity conditions. The behavior of that sequence, related to the Boeckx invariant $I_M$ and to the bi-Legendrian structure of $(M,\xi ,\varphi ,\eta ,g)$, is then studied. Finally we are able to define a canonical Sasakian structure on any contact metric $(\kappa ,\mu )$-space whose Boexkx invariant satisfies $|I_M|>1$.

To appear on: Pacific Journal of Mathematics

Cited by in corpus (6)

• Nullity conditions in paracontact geometry
• Ricci solitons in three-dimensional paracontact geometry
• Sasaki-Einstein and paraSasaki-Einstein metrics from (κ,μ)-structures
• A Study of Three-Dimensional Paracontact $(\kappa ,\mu ,\nu )$-SPACES
• The curvature tensor of (\ka,μ,ν)-contact metric manifolds
• On a remarkable class of paracontact metric manifolds