Jacobi osculating rank and isotropic geodesics on naturally reductive 3-manifolds

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dc.creatorGonzalez-Davila, J. C.
dc.date2007-12-13
dc.date.accessioned2026-07-07T08:49:00Z
dc.date.available2026-07-07T08:49:00Z
dc.descriptionWe study the Jacobi osculating rank of geodesics on naturally reductive homogeneous manifolds and we apply this theory to the 3-dimensional case. Here, each non-symmetric, simply connected naturally reductive 3-manifold can be given as a principal bundle over a surface of constant curvature, such that the curvature of its horizontal distribution is also a constant. Then, we prove that the Jacobi osculating rank of every geodesic is two except for the Hopf fibers, where it is zero. Moreover, we determine all isotropic geodesics and the isotropic tangent conjugate locus.
dc.description19 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0712.2132
dc.identifierhttp://arxiv.org/abs/0712.2132
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144146
dc.subjectDifferential Geometry
dc.subjectMetric Geometry
dc.subject53C20, 53C30, 53C22
dc.titleJacobi osculating rank and isotropic geodesics on naturally reductive 3-manifolds
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