New structures of golden type on the tangent bundle

The aim of our paper is to prove the existence of some types of almost (α, p)–golden structures, obtained as general natural lifts of the Riemannian metric from the base manifold M to the total space TM of the tangent bundle. We show that TM, endowed with a general natural almost (α, p)–golden structure (which is a generalisation of the golden structure) and with a general natural metric, is an almost (α, p)–golden Riemannian manifold if and only if the function coefficients of the almost (α, p)–golden structure are related to those of the metric by two systems of three equations each. When α = 1 we obtain five types of such manifolds and when α = -1 we show that TM is an almost (-1, p)–golden Riemannian manifold if and only if the function coefficients of the metric and of the (-1, p)–golden structure satisfy some proportionality relations.