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@article{877418,
author = {Zalabová, Lenka},
article_location = {Amsterdam},
article_number = {5},
keywords = {Cartan geometries; Parabolic geometries; |1|-graded geometries; Weyl structures; Symmetric spaces},
language = {eng},
issn = {0926-2245},
journal = {Differential Geometry and its Applications},
title = {Symmetries of parabolic geometries},
volume = {27},
year = {2009}
}
TY - JOUR
ID - 877418
AU - Zalabová, Lenka
PY - 2009
TI - Symmetries of parabolic geometries
JF - Differential Geometry and its Applications
VL - 27
IS - 5
SP - 605-622
EP - 605-622
PB - Elsevier Science
SN - 09262245
KW - Cartan geometries
KW - Parabolic geometries
KW - |1|-graded geometries
KW - Weyl structures
KW - Symmetric spaces
N2 - We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly |1|-graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of Weyl structures to discuss more interesting |1|-graded geometries which can carry a symmetry in a point with nonzero curvature. More concretely, we discuss the number of different symmetries which can exist at the point with nonzero curvature.
ER -
ZALABOVÁ, Lenka. Symmetries of parabolic geometries. \textit{Differential Geometry and its Applications}. Amsterdam: Elsevier Science, 2009, vol.~27, No~5, p.~605-622. ISSN~0926-2245.
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