Klein Geometries, Parabolic Geometries and Differential Equations of Finite Type
Journal of Lie Theory, Volume 18 (2008) no. 1, pp. 67-82
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 $G$.
@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},
doi = {10.5802/jolt.482},
zbl = {1198.53050},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.482/}
}
TY - JOUR AU - E. Abadoglu AU - E. Ortacgil AU - F. Öztürk TI - Klein Geometries, Parabolic Geometries and Differential Equations of Finite Type JO - Journal of Lie Theory PY - 2008 SP - 67 EP - 82 VL - 18 IS - 1 UR - https://jolt.centre-mersenne.org/articles/10.5802/jolt.482/ DO - 10.5802/jolt.482 ID - JOLT_2008_18_1_a4 ER -
%0 Journal Article %A E. Abadoglu %A E. Ortacgil %A F. Öztürk %T Klein Geometries, Parabolic Geometries and Differential Equations of Finite Type %J Journal of Lie Theory %D 2008 %P 67-82 %V 18 %N 1 %U https://jolt.centre-mersenne.org/articles/10.5802/jolt.482/ %R 10.5802/jolt.482 %F JOLT_2008_18_1_a4
E. Abadoglu; E. Ortacgil; F. Öztürk. Klein Geometries, Parabolic Geometries and Differential Equations of Finite Type. Journal of Lie Theory, Volume 18 (2008) no. 1, pp. 67-82. doi: 10.5802/jolt.482
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