高维球面曲线

ON HIGHER DIMENTIONAL SPHERICAL CURVES

本文研究高维球面曲线的性质.在给出一个特别的活动标架及其无穷小位移公式(定理1)之后,我们证明了高维球面曲线落于赤道上的一个充要条件(定理2).我们还给出了高维球面曲线的几个特征性质.

<ABSTRACT>We study, in this paper, the properties of a curve ?(s)in S^(n-1), a sphere in 1R^n. First, we give, on ?(s)?S^(n-1), a special moving frame and the formula for the infinitesimal change of the frame (Theorem 1). Then we obtain a necessary and sufficient condition for ?(s)to lie completely on S^(n-2) (Theorem 2). Finally, we turn to the curves in S~?, and give several results which characterizes the curvatures of a curve in S~?.