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2012•Birkhäuser Boston eBooksRequires access

Differential Geometry of Curves

Garret Sobczyk

Open publisher page 1 citations

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.

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What this paper is about

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.

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Available 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.

Key concepts: Differential geometry of curves, Differential geometry, Frenet–Serret formulas, Geometry, Surface (topology), Differential (mechanical device), Mathematics, Differential calculus

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