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Klein geometries, parabolic geometries and differential equations of finite type

Ender Abadoglu·Ercument Ortacgil
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Abstract

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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Ender Abadoglu, Ercument Ortacgil. 2009-12-04. Klein geometries, parabolic geometries and differential equations of finite type. https://arxiv.org/abs/math/0701254

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