Local Generalized Symmetries and Locally Symmetric Parabolic Geometries

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Authors: Gregorovič, J., Zalabová, L.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148627
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Local Generalized Symmetries and Locally Symmetric Parabolic Geometries / J. Gregorovič, L. Zalabová // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 25 назв. — англ.

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 ea...