On certain symmetries of $\mathbb R^3$ with a diagonal metric

TL;DR

This paper characterizes the symmetries of a three-dimensional Euclidean space equipped with a specific diagonal metric by identifying its Killing vector fields.

Contribution

It explicitly determines the Killing vector fields for a class of diagonal metrics on bcs^3, extending understanding of symmetries in non-standard geometric settings.

Findings

Explicit form of Killing vector fields for the given metric

Classification of symmetries based on the metric parameters

Insights into geometric invariances of diagonal metric spaces

Abstract

We determine Killing vector fields on the $3$-dimensional space $\mathbb R^3$ endowed with a special diagonal metric.