sigma09-098. 379KB Jun 04 2011 12:10:33 AM
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The main idea is to consider the Lax pair ( 4 ) as equations for algebraic curves with respect to the unknown variables of the Painlev´e equation.. For the elliptic case,
the general idea is, first, to determine the holonomy invariant distributions peculiar to that type and identify any covariantly constant or recurrent vector fields, second to
The Killing operator in Riemannian geometry provides a good example of a first order linear differential operator to which the reasoning above may be applied.. It is a
Key words: homogeneous spaces, weakly symmetric spaces, homogeneous spaces of posi- tive Euler characteristic, geodesic orbit spaces, normal homogeneous Riemannian
Elkin [12, 13] has studied equivalence of affine distributions on manifolds of dimension n ≤ 4 under diffeomorphisms of the underlying manifolds, resulting in local normal forms for
The purpose of this paper is to establish the most general formal setting for reformulating, whenever possible, basic properties of groups in terms of vector spaces,
In addition, these critical sections can be thought of as being the integral manifolds of certain kinds of integrable multivector fields or Ehresmann connections, defined in the
And thirdly, we need to get the results in uniform notations, for Section 4 , where we make a comparison of the general solutions of ( 2 ) and ( 3 ), taking into account that these
