A comprehensive review of golden Riemannian manifolds

TL;DR

This paper provides a comprehensive survey of golden Riemannian manifolds, summarizing a decade of research on their properties, structures, and applications in differential geometry.

Contribution

It offers an extensive review of recent developments in golden Riemannian manifolds, consolidating various research efforts into a single comprehensive survey.

Findings

Summarizes key properties of golden Riemannian manifolds.

Highlights applications in differential geometry.

Identifies future research directions.

Abstract

In differential geometry, the concept of golden structure, initially proposed by S. I. Goldberg and K. Yano in 1970, presents a compelling area with wide-ranging applications. The exploration of golden Riemannian manifolds was initiated by C. E. Hretcanu and M. Crasmareanu in 2008, following the principles of the golden structure. Subsequently, numerous researchers have contributed significant insights into golden Riemannian manifolds. The purpose of this paper is to provide a comprehensive survey on golden Riemannian manifold done over the past decade.