Geometric researches in complex analysis

点击翻译按钮获取中文摘要

The purpose of this research is to investigate complex analysis in the aspect of geometry and, moreover, to give applications of complex analysis to geometry. To these ends, we need to have interchanges of researchers in various fields of mathematics. We held various sympsiums many times and obtained many new results in these fields.H. Fujimoto succeeded in the constructions of hyperbolic hypersurfaces of degree 2^n in the n (【greater than or equal】3)-dimensional complex projective space. He also obtained some sufficient conditions for polynomials to be uniqueness polynomials. S. Mori, together with Y. Aihara, constructed many examples of holomorphic mappings into the complex projective space with pre-assinged positive deficiency. T. Ueda studied fixed points of polynomial automorphisms of C^n and showed that the sum of holomorphic Lefshetz indices vanishes for generalized Henon maps under some conditions. By introducing the notion of balayage vector potentials, H. Yamaguchi maked clear the importance of harmonic forms. H. Sato founded many kinds of Jorgensen groups. H. Kazama studied complex analytic cohomology groups of topologically trivial line bundles over 1-dimension complex torus and showed the existence of formal Hartogs-Laurent series associated with line bundles. A. Kodama investigated the conditions for domains whose boundary are strongly pseudo-convex excluding some singularities to become complete Riemannian manifolds with respect to Webster me trices.