The foliated structure of contact metric (k,μ)-spaces

CAPPELLETTI MONTANO, BENIAMINO

2009-01-01

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Abstract

In this paper we study the foliated structure of a contact metric (k,μ)-space. In particular, using the theory of Legendre foliations, we give a geometric interpretation to the Boeckx's classification of contact metric (k,μ)-spaces and we find necessary conditions for a contact manifold to admit a compatible contact metric (k,μ)-structure. Finally we prove that any contact metric (k,μ)-space M whose Boeckx invariant I_M is different from \pm 1 admits a compatible Sasakian or Tanaka-Webster parallel structure according to the circumstance that |I_M|>1 or |I_M|<1, respectively.