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

Year 2018, Volume: 21 Issue: 4, 967 - 970, 01.12.2018

Feyza Esra Erdoğan Cumali Yıldırım

https://doi.org/10.2339/politeknik.389629

Cited By: 11

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.

Keywords

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

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