Conformal Killing Vectors in Five-Dimensional Space

TL;DR

This paper derives solutions to the generalized Killing equation for a five-dimensional space with specific symmetry, identifying metric coefficients associated with conformal Killing vectors.

Contribution

It provides explicit solutions for conformal Killing vectors in five-dimensional space with initial symmetry, expanding understanding of symmetries in higher-dimensional geometries.

Findings

Solutions to the generalized Killing equation are obtained.

Explicit metric coefficients for these vectors are provided.

The work enhances the classification of symmetries in five-dimensional spaces.

Abstract

The solutions of generalized Killing equation have been obtained for line element with initial $t^2 \oplus so(3)$ symmetry. The coefficients of the metric $g$ corresponding to these vector fields are written down.