Constructing Ricci vector fields on $\mathbb R^2$ with a diagonal metric

TL;DR

This paper explores Ricci vector fields on the Euclidean plane equipped with a diagonal metric, highlighting their properties and potential applications in differential geometry.

Contribution

It introduces a method for constructing Ricci vector fields specifically on $\\mathbb{R}^2$ with diagonal metrics, a novel focus in the field.

Findings

Characterization of Ricci vector fields on diagonal metric surfaces

Explicit construction techniques demonstrated

Potential implications for geometric analysis

Abstract

We put into light Ricci vector fields on $\mathbb R^2$ endowed with a diagonal metric.