Journal of the Australian Mathematical Society

Research Article

HOMOGENEOUS AND H-CONTACT UNIT TANGENT SPHERE BUNDLES

G. CALVARUSOa1 and D. PERRONEa2 c1

a1 Dipartimento di Matematica ‘E. De Giorgi’, Università del Salento, 73100 Lecce, Italy (email: giovanni.calvaruso@unisalento.it)

a2 Dipartimento di Matematica ‘E. De Giorgi’, Università del Salento, 73100 Lecce, Italy (email: domenico.perrone@unisalento.it)

Abstract

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 $\tilde G$ is a Riemannian g-natural metric on T1M of Kaluza–Klein type, then $(T_1 M,\tilde \eta ,\tilde G)$ 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

  • primary 53C15; secondary 53C25;
  • 53D10

Keywords and phrases

  • two-point homogeneous spaces;
  • unit tangent sphere bundle;
  • g-natural metric;
  • H-contact spaces

Correspondence:

c1 For correspondence; e-mail: domenico.perrone@unisalento.it

Footnotes

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