Structures Induced on Hypersurfaces of Meta-Golden Riemannian Manifolds

Abstract

In this paper, our aim is to examine the hypersurfaces in almost meta-Golden Riemannian manifolds. First, the properties of the induced structure on a hypersurface by meta-Golden Riemannian structures were investigated. After that a necessary and sufficient condition for a hypersurface to be a meta-Golden Riemannian manifold in terms of invariant were obtained. Then, totally geodesic, minimal and totally umbilical hypersurfaces were analyzed in the meta-Golden Riemann manifold, respectively. Invariant and non-invariant hypersurfaces of meta-Golden Riemann manifolds were also characterized. The relationships between the eigenvalues of the golden structure and the invariant and non-invariant hypersurfaces of the meta-Golden Riemann manifolds were investigated. Finally an example of such hypersurfaces was given.