{ "id": "1003.1416", "version": "v1", "published": "2010-03-06T18:59:55.000Z", "updated": "2010-03-06T18:59:55.000Z", "title": "Geometric structures associated with a contact metric $(κ,μ)$-space", "authors": [ "Beniamino Cappelletti Montano", "Luigia di Terlizzi" ], "comment": "To appear on: Pacific Journal of Mathematics", "journal": "Pacific J. Math. 246 (2010), 257-292", "doi": "10.2140/pjm.2010.246.257", "categories": [ "math.DG" ], "abstract": "We prove that any contact metric $(\\kappa,\\mu)$-space $(M,\\xi,\\phi,\\eta,g)$ admits a canonical paracontact metric structure which is compatible with the contact form $\\eta$. We study such canonical paracontact structure, proving that it verifies a nullity condition and induces on the underlying contact manifold $(M,\\eta)$ a sequence of compatible contact and paracontact metric structures verifying nullity conditions. The behavior of that sequence, related to the Boeckx invariant $I_M$ and to the bi-Legendrian structure of $(M,\\xi,\\phi,\\eta,g)$, is then studied. Finally we are able to define a canonical Sasakian structure on any contact metric $(\\kappa,\\mu)$-space whose Boexkx invariant satisfies $|I_M|>1$.", "revisions": [ { "version": "v1", "updated": "2010-03-06T18:59:55.000Z" } ], "analyses": { "subjects": [ "53C12", "53C15", "53C25", "53C26", "57R30" ], "keywords": [ "geometric structures", "paracontact metric structures verifying nullity", "metric structures verifying nullity conditions" ], "tags": [ "journal article" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2010arXiv1003.1416C" } } }