Elements of infinitesimal Riemannian geometry (Q2770049)
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scientific article; zbMATH DE number 1702487
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Elements of infinitesimal Riemannian geometry |
scientific article; zbMATH DE number 1702487 |
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20 February 2002
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limited point
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generalized Frenet formulas
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Elements of infinitesimal Riemannian geometry (English)
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The nonstandard analysis approach in the paper follows that of \textit{E. Nelson} [Bull. Am. Math. Soc. 83, 1165-1198 (1977; Zbl 0373.02040)] and \textit{M. Goze} [Colloq., Cerisy-la-Salle/Fr. 1990, 402-413 (1992; Zbl 0778.03024)]. The aim of the paper is to compare some punctual and intrinsic geometrical objects defined by a non standard differential geometry on a curve or on a surface. The author extends the Frenet's formulas on a curve in the standard space and shows some difficulties which arise trying to work on standard surfaces.
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