On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds
Makaleler > Tam Makale · 2018
Yazarlar: Feyza Esra ERDOĞAN, Cumali Yıldırım
Journal of Polytechnic, Uluslararası, 2018
DOI: 10.2339/politeknik.389629
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 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.