Conformal Patterson-Walker metrics

• Autoři: HAMMERL Matthias; SAGERSCHNIG Katja; ŠILHAN Josef; TAGHAVI-CHABERT Arman; ŽÁDNÍK Vojtěch
• Rok publikování: 2019
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: The Asian Journal of Mathematics
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://www.intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0023/0005/a001/index.php
• Doi: https://doi.org/10.4310/AJM.2019.v23.n5.a1
• Klíčová slova: Differential geometry; Parabolic geometry; Projective structure; Conformal structure; Einstein metrics; Conformal Killing field; Twistor spinors
• Popis: The classical Patterson-Walker construction of a split-signature (pseudo-)Riemannian structure from a given torsion-free affine connection is generalized to a construction of a split-signature conformal structure from a given projective class of connections. A characterization of the induced structures is obtained. We achieve a complete description of Einstein metrics in the conformal class formed by the Patterson-Walker metric. Finally, we describe all symmetries of the conformal Patterson-Walker metric. In both cases we obtain descriptions in terms of geometric data on the original structure.

Související projekty

• Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku