Paracontact metric structures on the unit tangent sphere bundle

Abstract

Starting from $g$-natural pseudo-Riemannian metrics of suitable signature on the unit tangent sphere bundle $T_{1}M$ of a Riemannian manifold $(M,⟨,⟩)$, we construct a family of paracontact metric structures. We prove that this class of paracontact metric structures is invariant under $\mathcal{D}$-homothetic deformations, and classify paraSasakian and paracontact $(\kappa ,\mu )$-spaces inside this class. We also present a way to build paracontact $(\kappa ,\mu )$-spaces from corresponding contact metric structures on $T_{1}M$.

21 pages

Cited by in corpus (2)

• Ricci solitons in three-dimensional paracontact geometry
• Natural Ricci Solitons on tangent and unit tangent bundles