Meta‐Golden Riemannian manifolds

Abstract

The logarithmic spiral in nature has been given as an example of the golden ratio until now. But recently, it has been shown that this is not true, and the logarithmic spiral has actually been shown to provide the so‐called Meta‐Golden‐Chi ratio. Inspiring from Meta‐Golden‐Chi ratio, we introduce almost Meta‐Golden manifolds, give a characterization, provide examples, and investigate certain properties of Meta‐Golden structure. The integrability of almost Meta‐Golden structure is checked, and the relation of Meta‐Golden structure with curvature tensor field is examined. In addition, if the Meta‐Golden manifold has constant curvature, it is shown that such manifold is a flat space under certain conditions. This implies that there is a need for a new concept of sectional curvature in Meta‐Golden Riemannian manifolds.