Pascual Jordan's "Erweiterte Gravitationstheorie" - A Historical Analysis of its Mathematical Framework

Abstract: This paper aims to highlight Pascual Jordan's axiomatic definition of the covariant derivative, as set out in his 1952 textbook "Schwerkraft und Weltall". Developed in light of his \emph{Erweiterte Gravitationstheorie} - a projective reformulation of relativity theory that incorporates a variable gravitational constant - Jordan's definition resembles those in contemporary usage. The paper contextualises Jordan's work within the broader historical frameworks of differential geometry and projective relativity, with a particular focus on the Princeton relativity group led by Oswald Veblen and Luther Pfahl Eisenhart. It also provides a summary of Jordan's formalism, focusing particularly on his definition of the covariant derivative, as well as a brief history of the origin and development of the covariant derivative.