ON THE ELLIPTIC CURVES ARISING FROM 4-BAR MECHANISMS

被引：0
|
作者：
Raza, Zahid [1 ]
Nazir, Shaheen [2 ]
机构：
[1] Natl Univ Comp & Emerging Sci Lahore, Lahore, Pakistan
[2] Abdus Salam Int Ctr Theoret Phys, Trieste, Italy
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2012年 / 42卷 / 04期
关键词：
Elliptic curves; real points; 4-bar mechanisms;
D O I：
10.1216/RMJ-2012-42-4-1359
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the residual curve R and the Darboux curve R' associated to a virtual 4-bar mechanism are two smooth elliptic curves defined over R, isomorphic over C but not isomorphic over R, see Theorem 2. The same question seems to be open for elliptic curves coming from an actual 4-bar mechanism. In this case we show that the corresponding real curves R(R) and R' (R) are diffeomorphic, see Theorem 3.
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页码：1359 / 1365
页数：7
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