Klein Geometries, Parabolic Geometries and Differential Equations of Finite Type
Copyright policy )Klein Geometries, Parabolic Geometries and Differential Equations of Finite Type
We define the infinitesimal and geometric orders of an effective Klein geometry G/H. Using these concepts, we prove i) For any integer m>1, there exists an effective Klein geometry G/H of infinitesimal order m such that G/H is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of geometric order M defines a differential equation of order M+1 on G/H whose global solution space is G (Proposition 18).
17 pages
Mathematics - Differential Geometry, Differential geometry of homogeneous manifolds, Differential Geometry (math.DG), homogeneous space, jet, FOS: Mathematics, 22E46, 22F30, Homogeneous spaces
Mathematics - Differential Geometry, Differential geometry of homogeneous manifolds, Differential Geometry (math.DG), homogeneous space, jet, FOS: Mathematics, 22E46, 22F30, Homogeneous spaces
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