[Author]
 V. S. Kalnitsky

[Title]
 The Jacobi algebras classification on homogeneous manifolds

[AMS Subj-class]
 53D25 Geodesic flows

[Abstract]
 The problem of classification of the geodesic flows symmetries
 polynomial on velocity on the tungent bundle
 of a homogeneous manifold has the qualitative solution. The
 question is reduced to the straightforward calculation. 
 The idea of such procedure is not
 new, it is equations described earlier by the author which are.
 The key notion is the tensor equation monodromy group. The list of
 possible Jacobi algebras coincides with a number of conjugate
 classes of the monodromy representations in the group of affine
 symmetries of the universal cover space. Remarkably that for the
 flat connections this conclusion follows right from the algebraic
 structure of the Jacobi algebra. Here the calculation is fulfilled
 for some important cases.

[Keywords]
 Spray, symmetry

[Comments]
 This article is the part of the technical report (St.Petersburg
 Government and Ministry of Education RF No. PD03-1.1-27).
 English, LaTeX, 10 pp.

[Contact e-mail]
 skalnitsky@hotmail.com