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 $J^{2}=J+I,$ 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 submanifolds immersed 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.

Keywords

• Golden structure,Riemannian manifold,totally geodesics,normal induced structure,killing vector fields

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