PARA-BLASCHKE ISOPARAMETRIC SPACELIKE HYPERSURFACES IN LORENTZIAN SPACE FORMS

摘要

Let x : M-n -> M-1(n)+1(c) be an umbilic-free spacelike hypersurface in the (n+1)-dimensional Lorentzian space form M-1(n)+1(c). Three basic conformal invariants of M-n are the conformal 1-form C, the conformal second fundamental form B, and the Blaschke tensor A. The para-Blaschke tensor D-lambda = A + lambda B which is a linear combination of A and B for some constant lambda is a symmetric (0, 2)-tensor. A spacelike hypersurface is called a para-Blaschke isoparametric spacelike hypersurface if the conformal 1-form vanishes and the eigenvalues of the para-Blaschke tensor are constant. In this paper, we classify the para-Blaschke isoparametric spacelike hypersurfaces under the conformal group of M-1(n)+1(c).