On certain generalized isometries of the special orthogonal group

TL;DR

This paper investigates generalized isometries of the special orthogonal group that preserve various distance measures, extending previous structural results on spectral isometries.

Contribution

It generalizes the structural understanding of isometries of $SO(n)$ beyond spectral cases, encompassing a broader class of distance-preserving transformations.

Findings

Characterization of generalized isometries of $SO(n)$

Extension of previous spectral isometry results

Broader class of distance measures preserved

Abstract

In this paper we explore the structure of certain generalized isometries of the special orthogonal group $SO(n)$ which are transformations that leave any member of a large class of generalized distance measures invariant. This gives us a far-reaching generalization of the former structural result of T. Abe, S. Akiyama and O. Hatori concerning $c$-spectral isometries of the special orthogonal group.