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HOMOGENEOUS AND H-CONTACT UNIT TANGENT SPHERE BUNDLES
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 88 / Issue 3 / June 2010
- Published online by Cambridge University Press:
- 12 May 2010, pp. 323-337
- Print publication:
- June 2010
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- Article
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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.
is a Riemannian 
is 