A distance on the equivalence classes of spherical curves generated by deformations of type RI
A distance on the equivalence classes of spherical curves generated by deformations of type RI
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由 RI 型变形生成的球面曲线等价类上的距离
DOI：
10.1142/s0218216518500669
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
and Hiroko Murai
中科院分区：
文献类型：
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作者：
Yukari Funakoshi;Megumi Hashizume;Noboru Ito;Tsuyoshi Kobayashi;and Hiroko Murai
在本文中，我们介绍了 RI 型和环境同位素变形下球面曲线等价类的距离。我们得到一个估计其下限的不等式（定理 1）。在定理2中，我们证明，如果对于一对球面曲线and,and并且满足一定的技术条件，则可以仅由单个弱RIII获得。在定理3中，我们表明，如果满足其他条件，则环境同位素为球面曲线，该曲线是通过一系列特定的局部变形而实现的。
In this paper, we introduce a distanceon the equivalence classes of spherical curves under deformations of type RI and ambient isotopies. We obtain an inequality that estimate its lower bound (Theorem 1). In Theorem 2, we show that if for a pair of spherical curvesand,andandsatisfy a certain technical condition, thenis obtained fromby a single weak RIII only. In Theorem 3, we show that ifandsatisfy other conditions, thenis ambient isotopic to a spherical curve that is obtained fromby a sequence of a particular local deformations, which realizes.