Elements of infinitesimal Riemannian geometry
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.
scientific article; zbMATH DE number 1702487