Pseudo-Jacobi operators and Osserman lightlike hypersurfaces

Abstract

We study pseudo-Jacobi operators associated to algebraic curvature maps on lightlike hypersurfaces M and investigate conditions for an induced Riemann curvature tensor to be an algebraic curvature map on M. Two examples are provided with explicit determination of their pseudo-Jacobi operators. Finally, we introduce the notion of lightlike Osserman hypersurfaces and prove some characterization results.