We prove that any contact metric $(\kappa,\mu)$-space $M$ admits a canonical paracontact metric structure that verifies some compatibity conditions with the contact structure. We study this paracontact structure, proving that it satisfies a nullity condition and induces on the underlying contact manifold $M$ a sequence of compatible contact and paracontact metric structures satisfying nullity conditions. The behavior of that sequence is related to the Boeckx invariant $I_M$ and to the bi-Legendrian structure of $M$ associated to the original $(\kappa,\mu)$-structure. Finally we are able to define a canonical Sasakian structure on $M$ starting by the original metric $(\kappa,\mu)$-structure.

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

DI TERLIZZI, Luigia
2010-01-01

Abstract

We prove that any contact metric $(\kappa,\mu)$-space $M$ admits a canonical paracontact metric structure that verifies some compatibity conditions with the contact structure. We study this paracontact structure, proving that it satisfies a nullity condition and induces on the underlying contact manifold $M$ a sequence of compatible contact and paracontact metric structures satisfying nullity conditions. The behavior of that sequence is related to the Boeckx invariant $I_M$ and to the bi-Legendrian structure of $M$ associated to the original $(\kappa,\mu)$-structure. Finally we are able to define a canonical Sasakian structure on $M$ starting by the original metric $(\kappa,\mu)$-structure.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/101769
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