a1 Dipartimento di Matematica ‘E. De Giorgi’, Università del Salento, 73100 Lecce, Italy (email: firstname.lastname@example.org)
a2 Dipartimento di Matematica ‘E. De Giorgi’, Università del Salento, 73100 Lecce, Italy (email: email@example.com)
We prove that all g-natural contact metric structures on a two-point homogeneous space are homogeneous contact. The converse is also proved for metrics of Kaluza–Klein type. We also show that if (M,g) is an Einstein manifold and is a Riemannian g-natural metric on T1M of Kaluza–Klein type, then is H-contact if and only if (M,g) is 2-stein, so proving that the main result of Chun et al. [‘H-contact unit tangent sphere bundles of Einstein manifolds’, Q. J. Math., to appear. DOI: 10.1093/qmath/hap025] is invariant under a two-parameter deformation of the standard contact metric structure on T1M. Moreover, we completely characterize Riemannian manifolds admitting two distinct H-contact g-natural contact metric structures, with associated metric of Kaluza–Klein type.
(Received September 02 2009)
(Accepted February 01 2010)
2000 Mathematics subject classification
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The authors are supported by funds of the University of Salento and the MIUR (PRIN 2007).