
TL;DR
This paper investigates systems of symmetries in |1|-graded parabolic geometries, focusing on smooth, non-flat homogeneous cases, and demonstrates the existence of an invariant affine connection under certain conditions.
Contribution
It introduces the study of symmetry systems in |1|-graded parabolic geometries and proves the existence of invariant affine connections under weak assumptions.
Findings
Existence of invariant affine connection under weak conditions
Analysis of smooth systems of symmetries in |1|-graded geometries
Characterization of non-flat homogeneous geometries
Abstract
We study here systems of symmetries on --graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous --graded geometries. We show the existence of an invariant admissible affine connection under quite weak condition on the system.
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