Lax Tensors, Killing Tensors and Geometric Duality

TL;DR

This paper investigates Lax tensors in differential geometry, classifies two-dimensional metrics with symmetric Lax tensors, and explores their behavior under duality, including explicit examples like flat space and Rindler systems.

Contribution

It provides a classification of 2D metrics with symmetric Lax tensors and analyzes their properties under geometric duality, including explicit solutions for specific systems.

Findings

Classified all 2D metrics with symmetric Lax tensors.

Found Lax tensors for flat space and Rindler system.

Analyzed Lax tensors on dual metrics.

Abstract

The solution of the Lax tensor equations in the case $L_{\alpha\beta\gamma}=-L_{\beta\alpha\gamma}$ was analyzed. The Lax tensors on the dual metrics were investigated. We classified all two dimensional metrics having the symmetric Lax tensor $L_{\alpha\beta\gamma}$. The Lax tensors of the flat space, Rindler system and its dual were found.