On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds

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Politeknik Dergisi
Volume:21 Issue:4
On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds

On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds

Authors : Feyza Esra ERDOĞAN, Cumali YILDIRIM

Pages : 967-970

Doi:10.2339/politeknik.389629

View : 36 | Download : 9

Publication Date : 2018-12-01

Article Type : Research Paper

Abstract :The Golden Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. Precisely, we can say that an insert ignore into journalissuearticles values(1,1);-tensor field P on a m-dimensional Riemann manifold M , g is a Golden structure if it satisfies the equation P 2 = P + Id , where Id is identity map on M . Furthermore, g P X , Y = g X , P Y , the Riemannian metric is called P -compatible and M , g , P is named a Golden Riemannian manifold. The main purpose of the present paper is to study the geometry of Riemannian manifolds endowed with Golden structures. For this purpose, we study totally umbilical semi-invariant submanifold of the Golden Riemannian manifolds. Also, we obtain integrability conditions of the distributions and investigate the geometry of foliations.
Keywords : Semi invariant submanifolds, Golden Riemannian manifolds, totally umbilical submanifolds

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