On Submanifolds in a Riemannian Manifold with Golden Structure

Abstract

A golden Riemannian structure (J, g) on a Riemannian manifold is given by a tensor field J of type(1, 1) satisfying the golden section relation J2 = J + I, and a pure Riemannian metric g, that is a metric satisfying g(JX, Y) = g(X, JY). We investigate some fundamental properties of the induced structure on submanifoldsimmersed in golden Riemannian manifolds. We obtain effective relations for some induced structures on submanifolds of codimension 2. We also construct an example on submanifold of a golden Riemannian manifold.