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http://dx.doi.org/10.14477/jhm.2015.28.3.133

On the History of the Birth of Finsler Geometry at Göttingen  

Won, Dae Yeon (Dept. of Math., Duksung Women's Univ.)
Publication Information
Journal for History of Mathematics / v.28, no.3, 2015 , pp. 133-149 More about this Journal
Abstract
Arrivals of Hilbert and Minkowski at $G\ddot{o}ttingen$ put mathematical science there in full flourish. They further extended its strong mathematical tradition of Gauss and Riemann. Though Riemann envisioned Finsler metric and gave an example of it in his inaugural lecture of 1854, Finsler geometry was officially named after Minkowski's academic grandson Finsler. His tool to generalize Riemannian geometry was the calculus of variations of which his advisor $Carath\acute{e}odory$ was a master. Another $G\ddot{o}ttingen$ graduate Busemann regraded Finsler geometry as a special case of geometry of metric spaces. He was a student of Courant who was a student of Hilbert. These figures all at $G\ddot{o}ttingen$ created and developed Finsler geometry in its early stages. In this paper, we investigate history of works on Finsler geometry contributed by these frontiers.
Keywords
Finsler metric; Riemannian metric; calculus of variations; convexity; tensor calculus; P. Finsler; H. Busemann; C. Gauss; B. Riemann; H. Minkowski; D. Hilbert; C. $Carath\acute{e}odory$; R. Courant;
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Times Cited By KSCI : 1  (Citation Analysis)
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