Notes on symmetric conformal geometries

Jan Gregorovič and Lenka Zalabová

Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
Institute of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Branišovská 1760, 370 05 České Budějovice, Czech Republic


Abstract: In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In particular, we show that each symmetric conformal geometry is either locally flat or covered by a pseudo-Riemannian symmetric space, where the covering is a conformal map. We construct examples of locally flat symmetric conformal geometries that are not pseudo-Riemannian symmetric spaces.

AMSclassification: primary 53C35; secondary 53A30.

Keywords: conformal geometry, symmetric space, parallel Weyl tensor.

DOI: 10.5817/AM2015-5-287