Value distribution thieory of meromorphic mappings, in particular, uniqueness, degeneracy and normal families of meromorphic mappings

首席研究员Aihara研究了亚纯映射的唯一性问题，他研究了亚纯映射的代数依赖的传播。他给出了从复m-空间上的有限张解析覆盖空间到射影代数流形的亚纯映射依赖的一些准则及其应用(出现在名古屋数学中)。J.)。特别地，他给出了光滑椭圆曲线上的两个全纯映射由椭圆曲线的自同态代数相关的条件。他和研究人员Mori还给出了一个具有亏量的亚纯映射的构造(超曲面的亚纯映射的亏量，预印本)。Mori研究了亚纯映射的缺陷的消去问题，得到了消去定理。Kitagawa研究了等距浸入常平均曲率的3-球面S^3中的平坦环面的等距变形。因此，他得到了S^3中等距浸入的平坦环面的一个分类，它不允许等距变形。Kamada研究了紧复曲面上自对偶中立型Khaler度量的存在性问题，证明了具有一定S^1对称性的紧致自对偶中立型Khaler曲面是双全纯到其中一个阶为d[小于或等于]2的Hirzebruch曲面，并研究了关于复射线乘积的显式自对偶中立型Khaler度量的构造.

The head investigator Aihara has studied the uniqueness problem of meromorphic mappings.He has investigated the propagation of algebraic dependence of meromorphic mappings. He gave some criteria for dependence of meromorphic mappings from finite sheeted analytic covering spaces over the complex m-space into a projective algebraic manifold and their applications (to appear hi Nagoya Math. J.). In particular, he gave a condition that two holomorphic mappings into a smooth elliptic curve are algebraically related by endomorphisms of elliptic curve. He and a investigator Mori also gave a construction of meromorphic mappings with deficiencies (Deficiencies of meromorphic mappings of hypersurfaces, preprint). An investigator Mori studied an elimination problem of defects of meromorphic mappings and obtained elimination theorems.An investigator Kitagawa studied isometric deformations of flat tori isometrically immersed hi the 3-sphere S^3 with constant mean curvature. As a result, he obtained a classification of the flat tori isometrically immersed in S^3 which admit no isometric deformation. An investigator Kamada studied the existence problem for self-dual neutral Khaler metrics on compact complex surfaces, and proved that a compact self-dual neutral Khaler surface admitting a certain S^1 symmetry is biholomorphic to one of the Hirzebruch surfaces of rank d 【less than or equal】 2. He also studied a construction of explicit self-dual neutral Khaler metrics on the product of complex projective lines.