Journal of Lie Theory 18 (2008), No. 1, 067--082
Copyright Heldermann Verlag 2008
Klein Geometries, Parabolic Geometries and Differential Equations of Finite Type
Ender Abadoglu
Yeditepe Universitesi, Matematik Bölümü, 26 Agustos Yerlesimi, 81120 Kayisdagi -- Istanbul, Turkey
eabadoglu@yeditepe.edu.tr
Ercüment Ortacgil
Bogazici Universitesi, Matematik Bölümü, 34342 Bebek -- Istanbul, Turkey
ortacgil@boun.edu.tr
Ferit Öztürk
Bogazici Universitesi, Matematik Bölümü, 34342 Bebek -- Istanbul, Turkey
ferit.ozturk@boun.edu.tr
[Abstract-pdf]
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 $G$.
Keywords: Homogeneous space, jet.
MSC: 53C30
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