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

Öz

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.

Anahtar Kelimeler

• Semi-invariant submanifolds,Golden Riemannian manifolds,totally umbilical submanifolds

Kaynakça

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