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arXiv · 1309.4213

Paracontact metric structures on the unit tangent sphere bundle

Giovanni Calvaruso·Verónica Martín-Molina
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Abstract

Starting from $g$-natural pseudo-Riemannian metrics of suitable signature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,\langle,\rangle)$, 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 $T_1 M$.

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Giovanni Calvaruso, Verónica Martín-Molina. 2013-09-17. Paracontact metric structures on the unit tangent sphere bundle. https://doi.org/10.1007/s10231-014-0424-4

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