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Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature. Moreover, we show that if there is exactly one symmetry at each point, then the parabolic geometry is a generalization of an affine (locally) symmetric space.
Keywords: parabolic geometries; generalized symmetries; generalizations of symmetric spaces; automorphisms with fixed points; prolongation rigidity; geometric properties of symmetric parabolic geometries. 
@article{SIGMA_2017_13_a31,
     author = {Jan Gregorovi\v{c} and Lenka Zalabov\'a},
     title = {Local {Generalized} {Symmetries} and {Locally} {Symmetric} {Parabolic} {Geometries}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2017},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a31/}
}
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Jan Gregorovič; Lenka Zalabová. Local Generalized Symmetries and Locally Symmetric Parabolic Geometries. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a31/

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