First BGG operators on homogeneous conformal geometries

• Autoři: GREGOROVIČ Jan; ZALABOVÁ Lenka
• Rok publikování: 2023
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Classical and Quantum Gravity
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1088/1361-6382/acbc05
• Doi: http://dx.doi.org/10.1088/1361-6382/acbc05
• Klíčová slova: homogeneous conformal geometry; first BGG operator; conformal Killing tensors; twistor spinors; conformal Killing-Yano forms; Godel metric; conformal circles
• Popis: We study first BGG operators and their solutions on homogeneous conformal geometries. We focus on conformal Killing tensors, conformal Killing-Yano forms and twistor spinors in particular. We develop an invariant calculus that allows us to find solutions explicitly using only algebraic computations. We also discuss applications to holonomy reductions and conserved quantities of conformal circles. We demonstrate our result on examples of homogeneous conformal geometries coming mostly from general relativity.

Související projekty

• Symetrie a invariance v analýze, geometrickém modelování a teorii optimálního řízení