{"paper":{"title":"The foliated structure of contact metric $(\\kappa,\\mu)$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Beniamino Cappelletti Montano","submitted_at":"2009-03-31T18:28:29Z","abstract_excerpt":"In this paper we study the foliated structure of a contact metric $(\\kappa,\\mu)$-space. In particular, using the theory of Legendre foliations, we give a geometric interpretation to the Boeckx's classification of contact metric $(\\kappa,\\mu)$-spaces and we find necessary conditions for a contact manifold to admit a compatible contact metric $(\\kappa,\\mu)$-structure. Finally we prove that any contact metric $(\\kappa,\\mu)$-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 $|I_M|>1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.5534","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}