On Submanifolds in a Riemannian Manifold with Golden Structure

Authors : Mobin AHMAD, Mohammad Aamir QAYYOOM

Pages : 8-23

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Publication Date : 2019-06-30

Article Type : Research Paper

Abstract :A golden Riemannian structure $insert ignore into journalissuearticles values(J,g);$ on a Riemannian  manifold is given by a tensor field $J$ of type $insert ignore into journalissuearticles values(1,1);$ satisfying the golden section relation $J^{2}=J+I,$ and a pure Riemannian metric $g$, that is  a metric satisfying $ginsert ignore into journalissuearticles values(JX,Y);=ginsert ignore into journalissuearticles values(X,JY);.$ 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