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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
