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 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.