Differential Geometry of Curves

Garret Sobczyk
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Garret Sobczyk: Universidad de Las Américas, Departamento de Física y Matemáticas

Chapter Chapter 14 in New Foundations in Mathematics, 2013, pp 243-251 from Springer

Abstract: Abstract The study of the differential geometry of surfaces rightly begins with the study of curves, since a curve can be considered to be a 1-dimensional surface, and a more general surface can be considered to be the set of all curves which belong to the surface. In particular, the classical formulas of Frenet-Serret are derived for the moving frame along a curve. The study of the calculus of a k-surface, begun in the previous chapter, is also a part of differential geometry.

Keywords: Unit Speed Curve; Regular Reparametrization; Frenet-Serret Equations; Er Bel; Right-handed Orthonormal Frame (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-0-8176-8385-6_14

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