Osserman Conditions in Lightlike Warped Product Geometry

Abstract

In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study of lightlike warped product Osserman manifolds. For the coisotropic case with totally degenerates first factor, we prove that this class consists of Einstein and locally Osserman lightlike warped product.

Inequalities for Scalar Curvature and Shape Operator of an R-Lightlike Submanifold in Semi-Riemannian Manifold

“…In [7] the autors established some remarkable geometric roperties to ensure algebraicity of the induced Riemannian curvature tensor on lightlike Warped Product Manifolds. The same approach has been explored in [8] to present osserman conditions for lightlike warped product manifolds. Using rigging technical, the authors showed the nonexistence of stable currents in lightlike hypersurface of Lorentzian manifold and they has established some inequalities between the main extrinsic and intrinsic invariants on lightlike hypersurface in the Lorentzian manifold in [9] [10].…”