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HOMOGENEOUS AND H-CONTACT UNIT TANGENT SPHERE BUNDLES

Part of: Global differential geometry Symplectic geometry, contact geometry

Published online by Cambridge University Press:  12 May 2010

G. CALVARUSO  and
D. PERRONE
G. CALVARUSO
Affiliation:
Dipartimento di Matematica ‘E. De Giorgi’, Università del Salento, 73100 Lecce, Italy (email: giovanni.calvaruso@unisalento.it)
D. PERRONE*
Affiliation:
Dipartimento di Matematica ‘E. De Giorgi’, Università del Salento, 73100 Lecce, Italy (email: domenico.perrone@unisalento.it)
*
✉For correspondence; e-mail: domenico.perrone@unisalento.it
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Abstract

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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.

Keywords

two-point homogeneous spacesunit tangent sphere bundleg-natural metricH-contact spaces

MSC classification

Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D10: Contact manifolds, general
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 3 , June 2010 , pp. 323 - 337
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The authors are supported by funds of the University of Salento and the MIUR (PRIN 2007).

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