On Submanifolds in a Riemannian Manifold with Golden Structure

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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Turkish Journal of Mathematics and Computer Science-Cover

ISSN: 2148-1830
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: MATEMATİKÇİLER DERNEĞİ

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