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Constancy of Jacobi osculating rank of g.o. spaces of compact and non-compact type. (English) Zbl 1230.53045

The authors prove that the Jacobi osculating rank is not always constant for a non-naturally reductive g.o. space \(M\) that is either compact, or admits a transitive non-compact semisimple Lie group of isometries.

MSC:

53C30 Differential geometry of homogeneous manifolds
53C20 Global Riemannian geometry, including pinching
53C22 Geodesics in global differential geometry
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