General Natural Metallic Structure on Tangent Bundle

Abstract

In this paper, we study the natural lift types as complete and horizontal of a metallic structures on the tangent bundle of a Riemannian manifold and find some interesting results about structures, metric, distribution and the relationship between them. In the end, we introduce general natural lifts of a metallic structure and a semi-Riemannian manifold on the tangent bundle and get the conditions under which the tangent bundle endowed with such a metallic structure and a general natural lifted metric is a Riemannian manifold.