Classification of hypersurfaces with parallel Laguerre second fundamental form in R-n

摘要

Let x : M -> R-n be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of x under the Laguerre transformation group are the Laguerre metric g and the Laguerre second fundamental form B. In this paper, we classify all oriented hypersurfaces in R-n with a parallel Laguerre second fundamental form B. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.