LORENTZIAN ISOPARAMETRIC HYPERSURFACES IN Hn+11

in Lorentzian space forms and studied the Cartan identities. Later Hahn, 1984, generalized Nomizu’s work to the pseudo-Riemannian space forms and presented many examples. In general, the shape operator of a hypersurface in a pseudo-Riemannian space form may be not diagonalizable. This makes the isoparametric theory in pseudo-Riemannian space form different from that in Riemannian space forms. In 1985, Megid classified Lorentzian isoparametric hypersurfaces in Rn+11. He showed that there are three types of Lorentzian isoparametric hypersurfaces in Rn+11. Type I are exactly cylinders and umblic hypersurfaces while the other two types of hypersurfaces have properties close to cylinders and umblic hypersurfaces. Megid called them generalized cylinders and umblic hypersurfaces. In this paper, the local classification of Lorentzian isoparametric hypersurfaces in Hn+11 is obtaine