Article ID Journal Published Year Pages File Type
4606489 Differential Geometry and its Applications 2009 14 Pages PDF
Abstract
We 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 M3(κ,τ) over a surface of constant curvature κ, such that the curvature of its horizontal distribution is a constant τ>0, with τ2≠κ. Then, we prove that the Jacobi osculating rank of every geodesic of M3(κ,τ) is two except for the Hopf fibers, where it is zero. Moreover, we determine all isotropic geodesics and the isotropic tangent conjugate locus.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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