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.
Highlights
The Riemann curvature tensor is one of the central concepts in the mathematical field of differential geometry
For the coisotropic case with totally degenerates first factor, we prove that this class consists of Einstein and locally Osserman lightlike warped product
Motivated by the recent works on lightlike geometry, we consider in this paper lightlike warped productmanifolds and examine Osserman conditions depending on geometric properties of the factors
Summary
The Riemann curvature tensor is one of the central concepts in the mathematical field of differential geometry. It assigns a tensor to each point of a (semi-)Riemannian manifold that measures the extent to which the metric tensor is not locally isometric to that of Euclidean space. Curvature tensor is a central mathematical tool in the theory of general relativity and gravity. The geometry of a pseudo-Riemannian manifold (M , g ) is the study of the curvature R ∈ ⊗4T *M which is defined by the Levi-Civita connection ∇. Gilkey studied geometric properties of natural operators
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