Recent Advances in Metallic Riemannian Geometry: A Comprehensive Review

TL;DR

This paper provides a comprehensive review of recent developments in metallic Riemannian geometry, highlighting its foundational concepts, recent advances, and potential applications within differential geometry.

Contribution

It synthesizes recent research progress in metallic Riemannian manifolds, emphasizing new theoretical insights and expanding the understanding of this emerging field.

Findings

Identification of new properties of metallic Riemannian manifolds

Development of novel applications in differential geometry

Summarization of recent research trends and future directions

Abstract

Metallic structures, introduced by V. de Spinadel in 2002, opened a new avenue in differential geometry. Building upon this concept, C. E. Hre\c{t}canu and M. Crasmareanu laid the foundation for metallic Riemannian manifolds in 2013. The field's rich potential and diverse applications have since attracted significant research efforts, leading to a wealth of valuable insights. This review delves into the latest advances in metallic Riemannian geometry, a rapidly progressing area within the broader field of differential geometry.