射影变形Legendrian曲面
Projectively deformable Legendrian surfaces
摘要：
考虑五维复射影空间中具有标准齐次切触结构的浸入勒让德曲面。引入了一类四阶射影Legendrian变形\emph{$\,Ψ$-deformation}，并给出了允许最大三参数变形族的曲面的微分几何刻划.最大$\, Ψ$ -变形曲面的两个显式的例子构造;第一个是由Legendrian映射从$\, \PP^2$炸毁在三个不同的共线点，这是一个嵌入远离-2-曲线和退化到一个点沿-2-曲线。第二个是一个Legendrian嵌入的6度del Pezzo表面，$\, \PP^2$炸毁在三个非共线点。在这两种情况下，勒让德映射都是由通过三点的三次系统给出的，它是反正则系统的一个子系统。
英文摘要：
Consider an immersed Legendrian surface in the five dimensional complex projective space equipped with the standard homogeneous contact structure. We introduce a class of fourth order projective Legendrian deformation called \emph{$\,Ψ$-deformation}, and give a differential geometric characterization of surfaces admitting maximum three parameter family of such deformations. Two explicit examples of maximally $\, Ψ$-deformable surfaces are constructed; the first one is given by a Legendrian map from $\, \PP^2$ blown up at three distinct collinear points, which is an embedding away from the -2-curve and degenerates to a point along the -2-curve. The second one is a Legendrian embedding of the degree 6 del Pezzo surface, $\, \PP^2$ blown up at three non-collinear points. In both cases, the Legendrian map is given by a system of cubics through the three points, which is a subsystem of the anti-canonical system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
