关于空间型中闭曲线的平均绝对曲率

ON MEAN ABSOLUTE GEODESIC CURVATURE OF CLOSED CURVES IN SPACE FORMS

对 2维空间型中相应的一些主要结果进行了推广 .在n维空间型中 ,比较了任一闭曲线和包含此闭曲线的凸测地球边界上一个大圆的平均绝对曲率 .这在一定意义下描述了闭曲线在n维空间型中的弯曲程度 .

The relative main results in 2-dimensional space forms are generalized. The goal is, in n-dimensional space forms, to compare the mean absolute curvature of a closed curve C with that of a big circle in the boundary of a convex geodesic ball containing the curve C. This can describe the extent to which the closed curve bends in n-dimensional space forms.