Abstract
Concurrent vector fields lying on lightlike hypersurfaces of a Lorentzian manifold are investigated. Obtained results dealing with concurrent vector fields are discussed for totally umbilical lightlike hypersurfaces and totally geodesic lightlike hypersurfaces. Furthermore, Ricci soliton lightlike hypersurfaces admitting concurrent vector fields are studied and some characterizations for this frame of hypersurfaces are obtained.
Highlights
Applications of concurrent vector fields have been investigated and Riemannian and semi-Riemannian manifolds equipped with concurrent vector fields have been intensely studied by various authors
The main purpose of this paper is to investigate concurrent vector fields on lightlike hypersurfaces and Ricci solitons lightlike hypersurfaces of a Lorentzian manifold
The second main problem is that the Ricci tensor of any lightlike hypersurface is not symmetric
Summary
Applications of concurrent vector fields have been investigated and Riemannian and semi-Riemannian manifolds equipped with concurrent vector fields have been intensely studied by various authors (cf [2,3,4,5,6,7]). A Riemannian manifold ( M, g) with a metric tensor g is called a Ricci soliton if there exists a smooth vector field v tangent to M satisfying the following equation: Accepted: 24 December 2020. The second main problem is that the Ricci tensor of any lightlike hypersurface is not symmetric In this case, the Ricci soliton equation loses its geometric and physical meanings. To get rid of this problem, we investigate this equation on lightlike hypersurfaces with the genus zero screen distribution whose Ricci tensor is symmetric
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