ON DEMOULIN TRANSFORMS OF PROJECTIVE MINIMAL SURFACES(III)
ON DEMOULIN TRANSFORMS OF PROJECTIVE MINIMAL SURFACES(III)
复制标题
论射影极小曲面的德穆兰变换（三）
DOI：
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发表时间：
1957
期刊：
影响因子：
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通讯作者：
B. Su
中科院分区：
文献类型：
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作者：
B. Su
本文是前一篇文章的续篇，在前一篇文章中，我们考虑了与射影极小曲面S和它的一个D-变换（？）在空间S_5中存在相应的拉普拉斯序列（？）（W）和（？）如果我们构造（W）的密切线性复形在S_5中的第二个象，即超平面（？）对于Klein超二次曲面Q，则点P必属于一个拉普拉斯序列（？）（P）其中每个点都是前一个点沿u方向的沿着变换。以类似的方式，我们获得另一个拉普拉斯序列（？）证明了（P）和（P）可以由Godeaux序列（？）（L）和（？）的S和（？）作为连接点的交点，即（？）（n= 1，2，...），点（？）和（？）在85中给出了S的Demoulin四边形的两条边在（？）我们用（？）和（？）同余（W）和（W）的第二焦面，使得它们是S的第二D变换。是对应于对（（？））的沿拉普拉斯序列（W）的方向v的第二沿着变换，(?))和Laplace序列（？）对应于（S，（？））类似地是对应于（？）的拉普拉斯序列（W）沿u方向的第二次变换。讨论了Godeaux二次曲面（？）和（？）曲面S，（？）和（？）例如，Φ_n和（？）四点接触，使得Φ_n和（？）也触及其中两个，Φ_n和（？）在剩下的两个点。
The present paper is a sequel to a previous one in which we have consi-dered the two rectilinear congruences W associated with a projective minimalsurface S and one of its D-transforms(?).In the space S_5 there are corres-ponding Laplace sequences (?)(W)and(?)If we construct the second image in S_5 of the osculating linear complex of(W),that is,the pole P of the hyperplane(?)with respect tothe Klein hyperquadric Q,then the point P must belong to a Laplace sequence(?)(P)where every point is the transform of the preceding along the sense u.In asimilar way we obtain another Laplace sequence(?)where every point is the transform of the preceding along the same sense.It is shown that(P)and(P)can be obtained from the Godeaux sequences(?)(L)and(?)of S and(?)as intersections of joins,namely,(?)(n=1,2,…).The points(?)and(?)in 85 are the images of two sides of Demoulinquadrilateral of S which intersect each other at the corresponding point of(?).We denote by(?)and(?)the second focal sheets of the congruences(W)and(W),so that they are the second D-transforms of S.The Laplace sequence(W)corresponding to the pair(S,(?))is the second transform along the senseν of the Laplace sequence(W)corresponding to the pair((?),(?))and theLaplace sequence(?)corresponding to(S,(?))is similarly the second transformalong the sense u of the Laplace sequence(W)corresponding to((?)).Several remarkable relations between the sequences of Godeaux quadrics(?)and(?)of the surfaces S,(?)and(?)are obtained.For example,Φ_n and(?)touch at four points such that Φ_n and(?)alsotouch at two of them,and Φ_n and(?)at the remaining two points.