Geometric properties of homogeneous parabolic geometries with generalized symmetries

• Autoři: GREGOROVIČ Jan; ZALABOVÁ Lenka
• Rok publikování: 2016
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Differential Geometry and its Applications
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Doi: http://dx.doi.org/10.1016/j.difgeo.2016.09.008
• Obor: Obecná matematika
• Klíčová slova: Homogeneous parabolic geometries; Generalized symmetries; Holonomy reductions; Correspondence and twistor spaces; Invariant distributions; Invariant Weyl connections
• Popis: We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic geometries, we prove that the reductions correspond to known generalizations of symmetric spaces. In addition, we illustrate our results on an explicit example and provide a complete classification of possible non-trivial cases.

Související projekty

• Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku