ON THE INTEGRAL CURVATURE OF A CURVILINEAR POLYGON

<正> 1.In a recent papert on the theory of a closed space curve,theauthor has obtained among others the following result:If a closedspace curve C has an angular point of an interior angle θ,then theintegral curvature of C is not less than π+θ,or in other words:ifdenotes the curvature of C,then∮（c）kds≥π+θ.At the end ofthe same paper we have proposed a more general problem:Whatwill be the lower bound of the integral curvature∮（v）kds if the closedspace curve C has n（n>1）angular points?In the present paper,itis shown that the answer there conjectured is affirmative.By a cur-vilinear polygon we mean,in what follows,a closed space curve witha finite nuraber of angular points.A theorem for a curvilinearpolygon in aa ordinary space is proved with its generalization in aEuclidean space of higher dimensions.