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Contribution to the history of 19th century theory of geodesics. (Contribution à l’histoire de la théorie des géodésiques au XIX\(^ e\) siècle.) (French) Zbl 0842.01008

The author gives a short outline on the early history of geodesics. During the 19th century the problem of geodesics was often connected with questions of dynamics and mechanics, as examples there are mentioned Liouville, Darboux, Jacobi and Poincaré. After Gauss’ main contribution in 1828 many authors were interested in geodesics on surfaces of the second degree: Minding, Liouville, Jacobi, Michael Roberts, Chasles. While these authors had adopted a local point of view, Sturm used a global one, and with him Jacobi, Bonnet, Christoffel, Beltrami, Bertrand, von Mangoldt, Darboux, von Braunmühl, and Poincaré. All these investigations are closely connected with the theory of differential equations. Because of the fact that the sign of the curvature influences the results, Hadamard and Poincaré also examined geodesics on surfaces of purely positive or purely negative curvature.
Reviewer: K.Reich (Wentorf)

MSC:

01A55 History of mathematics in the 19th century
53-03 History of differential geometry
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