Legendre foliations on contact metric manifolds : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University

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dc.contributor.authorJayne, Nicola
dc.date.accessioned2012-07-03T23:54:43Z
dc.date.available2012-07-03T23:54:43Z
dc.date.issued1992
dc.description.abstractThis thesis develops the theory of Legendre foliations on contact manifolds by associating a contact metric structure with a contact manifold and investigating Legendre foliations on the resultant contact metric manifold. The contact metric structure introduces a metric for the Legendre foliation which enables us to study the curvature properties of a Legendre foliation, furthermore when this metric is bundle-like we have a semi-Riemannian foliation hence we can define a semi-Riemannian Legendre foliation and study its properties. We use the invariant Π as defined by Pang to define a family of contact metric structures for a non-degenerate Legendre foliation and from this family we pick out a unique contact metric structure the canonical contact metric structure. Furthermore a canonical contact metric structure is identified for a flat Legendre foliation and shown to be a Sasakian structure. Under some circumstances a Legendre foliation on a contact metric manifold has a second Legendre foliation, the conjugate Legendre foliation, associated with it. We investigate the conditions for the existence and the properties of the conjugate Legendre foliation. By using a definition similar to that of a Legendre foliation on a contact metric manifold we conclude this thesis by defining a complex Legendre foliation on a complex contact metric manifold and beginning an investigation of its properties.en
dc.identifier.urihttp://hdl.handle.net/10179/3554
dc.language.isoenen
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectLegendre foliationsen
dc.subjectContact manifoldsen
dc.subjectLegendre polynomialsen
dc.titleLegendre foliations on contact metric manifolds : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey Universityen
dc.typeThesisen
massey.contributor.authorJayne, Nicolaen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorMassey Universityen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophy (Ph.D.)en
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