Global inequalities for curves and surfaces in three-space

Summary The aim of the paper is to give upper bounds for the total curvature of smooth curves and surfaces embedded in euclidean space, in terms of other global geometric characters; in particular, for a plane curve , we prove the inequality K() < (2 + f()d()/2), where d() is the geometric degree of and f() is the number of its inflection points. In the case of a surface S, a bound is given in terms of the genus g(S), the number of components of the parabolic points on S and the geometry of its apparent contour.