Abstract
Transversal lightlike submanifolds of metallic semi-Riemannian manifolds
Highlights
Lightlike submanifolds are one of the most interesting topics in differential geometry
Since the induced metric is degenerate on lightlike submanifolds, the tools which are used to investigate the geometry of submanifolds in Riemannian case are not favorable in semi-Riemannian case and so the classical theory can not be used to define any induced object on a lightlike submanifold
In order to resolve the difficulties that arise during studying lightlike submanifolds, they introduced a non-degenerate distribution called screen distribution to construct a lightlike transversal vector bundle which does not intersect to its lightlike tangent bundle
Summary
Lightlike submanifolds are one of the most interesting topics in differential geometry. Metallic structures on Riemannian manifolds allow many geometric results to be given on a submanifold. Metallic structure on the ambient Riemannian manifold provides important geometrical results on the submanifolds, since it is an important tool while investigating the geometry of submanifolds. Many authors have studied Golden Riemannian manifolds and their submanifolds in recent years (see [1, 2, 3, 7, 8, 9, 23]). Considering given brief above, in this paper, we introduce transversal lightlike submanifolds of Metallic semi-Riemannian manifolds and studied their differential geometry.
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