Invariant submanifolds in golden Riemannian manifolds

Authors : Erol KILIÇ, Mustafa GÖK, Sadık KELEŞ

Pages : 1119-1132

Doi:10.31801/cfsuasmas.635434

View : 9 | Download : 6

Publication Date : 2020-12-31

Article Type : Research Paper

Abstract :In this paper, we study invariant submanifolds of a golden Riemannian manifold with the aid of induced structures on them by the golden structure of the ambient manifold. We demonstrate that any invariant submanifold in a locally decomposable golden Riemannian manifold leaves invariant the locally decomposability of the ambient manifold. We give a necessary and sufficient condition for any submanifold in a golden Riemannian manifold to be invariant. We obtain some necessary conditions for the totally geodesicity of invariant submanifolds. Moreover, we find some facts on invariant submanifolds. Finally, we present an example of an invariant submanifold.
Keywords : Invariant Submanifold, Golden Structure, Golden Riemannian Manifold