An Introduction To Curve Theory In R～n

In this thesis,following the ideas of classical differential geometry in R~3,we discuss regular curves in R~n.From the beginning of definition of regular curves,we introduce the natural para-metrization and Frenet-Serret Formula of regular curves.Then,by the Formula,we give calculation formulas of regular curves' curvatures ,and discuss the general helices and flatness of curves in R~n,finally we prove a geometry inequality of curvatures and arc length.