Riemannian Center of Mass and so called karcher mean

TL;DR

This paper discusses the historical development of the Riemannian center of mass, also known as the Karcher mean, clarifying its origins and addressing the renaming and referencing issues that arose in later literature.

Contribution

It provides a historical account of the Riemannian center of mass and clarifies the origin of the term Karcher mean, correcting misconceptions about its naming and references.

Findings

The Riemannian center of mass was constructed in 1973.

It was successfully applied with refined estimates between 1974-1981.

The term 'Karcher mean' was introduced around 1990 without proper attribution.

Abstract

The Riemannian center of mass was constructed in [GrKa] (1973). In [GKR1, GKR2, Gr, Ka, BuKa] (1974-1981) it was successfully applied with more refined estimates. Probably in 1990 someone renamed it without justification into karcher mean and references to the older papers were omitted by those using the new name. As a consequence newcomers started to reprove results from the above papers. - Here I explain the older history.