Author/Authors :
erdoğan, feyza esra adıyaman üniversitesi - eğitim fakültesi - matematik ve fen bilimleri eğitimi bölümü, Turkey , yildirim2, cumali inönü üniversitesi - fen edebiyat fakültesi - matematik bölümü, Turkey
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 𝑃̅ on a m-dimensional Riemann manifold (𝑀̅,𝑔̅) is a Golden structure if it satisfies the equation 𝑃̅2=𝑃̅+𝐼𝑑, where 𝐼𝑑 is identity map on 𝑀̅. Furthermore, 𝑔̅(𝑃̅ 𝑋,𝑌)=𝑔̅(𝑋,𝑃̅ 𝑌), the Riemannian metric is called 𝑃̅-compatible and (𝑀̅,𝑔̅,𝑃̅ ) 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.
NaturalLanguageKeyword :
Semi , invariant submanifolds , Golden Riemannian manifolds , totally umbilical submanifolds
