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- W614238217 abstract "The theory of transformation groups plays an important role in differential geometry. In this article, the author shows how the theory had been applied to research of the geometry. To do it, we pay attention to Killing’s paper in 1892, and compare it with Lie’s research in 1890. We also refer to killing’s other works and his background of study. Finally we conclude that his treatise of 1892 is the earliest work where the transformation groups were in contact with differential geometry. But Killing dealt with only a case of locally non-Euclidean spaces. Killing equations, which appeared in his 1892 paper, were not tools in differential geometry until Bianchi applied them to Riemannian spaces." @default.
- W614238217 created "2016-06-24" @default.
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- W614238217 date "2006-11-30" @default.
- W614238217 modified "2023-09-23" @default.
- W614238217 title "The Contact of Differential Geometry and Continuous Groups of Transformations : W. Killing's Ueber die Grundlagen der Geometrie" @default.
- W614238217 hasPublicationYear "2006" @default.
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