Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-22T12:05:43.096Z Has data issue: false hasContentIssue false
  • English
  • Français

On Holomorphic Maps into a Real Lie Group of Holomorphic Transformations

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

1. Introduction. Let M, N be complex manifolds and G be a group of holomorphic automorphisms of N. In [3] (c.f. p. 74) W. Kaup introduced the notion of holomorphic maps into a family of holomorphic maps between complex spaces. By definition, a map g: M→G is holomorphic if and only if the induced map g̃(x, y): = g(x) (y) (x∈M, y∈N) of M×N into N is holomorphic in the usual sense. The purpose of this note is to give a description of a holomorphic map of a connected complex manifold M into G. We show first the existence of the maximum connected Lie subgroup G0 of G which is a complex Lie transformation group of N.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 40 , December 1970 , pp. 139 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Cartan, H., Sur les fonctions de n variables complexes: Les transformations du produit topologique de deux domaines bornes, Bull. Soc. math. France 64(1936), 37–48.CrossRefGoogle Scholar
[2] Fujimoto, H., On the automorphism group of a holomorphic fiber bundle over a complex space, Nagoya Math. J., 37(1970),91–106.Google Scholar
[3] Kaup, W., Infinitesimale Transformationsgruppen komplexer Raume, Math. Ann., 160 (1965), 72–92.Google Scholar
[4] Matsushima, Y. and Morimoto, A., Sur certains espaces fibres holomorphes sur une variete de Stein, Bull. Soc. math. France, 88(1960), 137–155.Google Scholar