Hypersurfaces with parallel para-Laguerre tensor in Rn

Let x:MRn be an (n-1)-dimensional hypersurface with vanishing Laguerre form in Rn, B be the Laguerre second fundamental form and L be the Laguerre tensor of the immersion x. We define a symmetric (0, 2) tensor D=L+B which is so-called the para-Laguerre tensor of x, where is a constant. If delta D=0, we say that x is of parallel para-Laguerre tensor, where delta is the Levi-Civita connection of the Laguerre metric g. An eigenvalue of the para-Laguerre tensor is called a para-Laguerre eigenvalue of x. The aim of this paper is to classify all oriented hypersurfaces in Rn with parallel para-Laguerre tensor or with three distinct constant para-Laguerre eigenvalues one of which is simple. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim