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On Holomorphic Maps into a Real Lie Group of Holomorphic Transformations
Published online by Cambridge University Press: 22 January 2016
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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.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1970
References
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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
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