摘要
本文目的是研究两卵形弧间的等距对应，所得的主要结果是下列两定理：定理设Ｃ和Ｃ￣＊是两条正则的卵形线，它们的长度相等，Ｃ→Ｃ￣＊是等距映射，则在Ｃ上有４个不同的点Ａ１、Ａ２、Ａ３、Ａ４使Ｃ在Ａ＿ｉ的曲率等于Ｃ＊在＝１，２，３，４．）。定理设Ｃ和Ｃ￣＊都是以Ａ、Ｂ为端点的卵形弧，它们的长度相等；Ｃ→Ｃ￣＊是等距映射使；Ｍ为Ｃ上一点；对于ＡＭ上任Ｐ有对ＭＢ上任一点心Ｐ有．则α＊≤α，β≥β＊其中α（α＊）是Ｃ（Ｃ￣＊）在Ａ的弦切角，β（β￣＊）是Ｃ（Ｃ￣＊）在Ｂ的弦切角。
In this paper,we study the isometric correspondence between two oval arcs. The main results are the following theorems:Theorem Let C and C* be two regular ovals with the same legth,an isometric correspondence between C and C*. Then there are 4 points A1,A2,A3,A4 on C such that the curvature of C at A1 is equal to the curvature of C* at (i=1,2,3,4.).Theorem Let C and C* be two oval arcs with the same length and the same end points A, B;M a point on C; an isometric mapping such that (P)) for each point on AM and k(P)≤k((P)) for each point on MB.Then α≤α,β*≥β, where α(α*) is the angle between the tangent to C(C*) at A and AB,β(β*) is the angle between the tangent to C(C*)at B and BA.
