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A Classification of Homogeneous Surfaces

Published online by Cambridge University Press:  20 November 2018

A. T. Huckleberry  and
E. L. Livorni
A. T. Huckleberry
Affiliation:
University of Notre Dame, Notre Dame, Indiana
E. L. Livorni
Affiliation:
University of Notre Dame, Notre Dame, Indiana
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Throughout this paper a surface is a 2-dimensional (not necessarily compact) complex manifold. A surface X is homogeneous if a complex Lie group G of holomorphic transformations acts holomorphically and transitively on it. Concisely, X is homogeneous if it can be identified with the left coset space G/H, where if is a closed complex Lie subgroup of G. We emphasize that the assumption that G is a complex Lie group is an essential part of the definition. For example, the 2-dimensional ball B2 is certainly “homogeneous” in the sense that its automorphism group acts transitively. But it is impossible to realize B2 as a homogeneous space in the above sense. The purpose of this paper is to give a detailed classification of the homogeneous surfaces. We give explicit descriptions of all possibilities.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 5 , 01 October 1981 , pp. 1097 - 1110
Copyright
Copyright © Canadian Mathematical Society 1981

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