Klein geometries, parabolic geometries and differential equations of finite type

Details Klein geometries, parabolic geometries and differential equations of finite type Klein geometries, parabolic geometries and differential equations of finite type

2007-01-09

arxiv.org/abs/math/0701254v2

Mathematics

Differential Geometry

17 pages

Scientific paper

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).

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