Klein geometries, parabolic geometries and differential equations of finite type
Differential Geometry
2009-12-04 v2
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).
Keywords
Cite
@article{arxiv.math/0701254,
title = {Klein geometries, parabolic geometries and differential equations of finite type},
author = {Ender Abadoglu and Ercument Ortacgil},
journal= {arXiv preprint arXiv:math/0701254},
year = {2009}
}
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17 pages