Geodesic
Klein Geometries, Parabolic Geometries and Differential Equations of Finite Type
Journal of Lie Theory, Tome 18 (2008) no. 1, pp. 67-82

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Zbl   arXiv

We define the infinitesimal and geometric orders of an effective Klein geometry $G/H$. Using these concepts, we prove (i) For any integer $m\geq 2$, there exists an effective Klein geometry $G/H$ of infinitesimal order $m$ such that $G/H$ is a projective variety. (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 $G$.
Classification : 53C30
Mots-clés : Homogeneous space, jet 
E. Abadoglu; E. Ortacgil; F. Öztürk. Klein Geometries, Parabolic Geometries and Differential Equations of Finite Type. Journal of Lie Theory, Tome 18 (2008) no. 1, pp. 67-82. http://geodesic.mathdoc.fr/item/JOLT_2008_18_1_a4/
@article{JOLT_2008_18_1_a4,
     author = {E. Abadoglu and E. Ortacgil and F. \"Ozt\"urk},
     title = {Klein {Geometries,} {Parabolic} {Geometries} and {Differential} {Equations} of {Finite} {Type}},
     journal = {Journal of Lie Theory},
     pages = {67--82},
     year = {2008},
     volume = {18},
     number = {1},
     zbl = {1198.53050},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2008_18_1_a4/}
}
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