Journals / Politeknik Dergisi / 2018 / Cilt: 21 - Sayı: 4
On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds
- Journal
- Politeknik Dergisi
- Pages
- 967–970
- DOI
- —
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 (1,1)-tensor field on a m-dimensional Riemann manifold is a Golden structure if it satisfies the equation , where is identity map on . Furthermore, , the Riemannian metric is called -compatible and 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.
Özet
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 (1,1)-tensor field on a m-dimensional Riemann manifold is a Golden structure if it satisfies the equation , where is identity map on . Furthermore, , the Riemannian metric is called -compatible and 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.