compact Riemann surfaces上的投射结构和投射丛
Projective structures and projective bundles over compact Riemann surfaces
摘要：
利用PGL（2，C）中的一个具有转移函数的图集，给出亏格为g的紧致Riemann曲面X上的一个射影结构.等价地，投射结构由X上的投射sl（2，C）-丛给出，该丛配备有一个截面s和一个叶理F，该叶理F都横向于纤维和截面s。从后者的几何束图片，我们调查的经典问题和结果的射影结构。我们将给出一个完整的描述投影（实际上是仿射）结构的环面与明确的flierated束图像。
英文摘要：
A projective structure on a compact Riemann surface X of genus g is given by an atlas with transition functions in PGL(2,C). Equivalently, a projective structure is given by a projective sl(2,C)-bundle over X equipped with a section s and a foliation F which is both transversal to the fibers and the section s. From this latter geometric bundle picture, we survey on classical problems and results on projective structures. We will give a complete description of projective (actually affine) structures on the torus with an explicit versal family of foliated bundle picture.
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