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Lecture Notes in Mathematics

By: JÃ¶rg Winkelmann

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Paperback | 6 April 1995

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248 Pages

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23.39 x 15.6 x 1.32

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This book provides a classification of all three-dimensional complex manifolds for which there exists a transitive action (by biholomorphic transformations) of a real Lie group. This means two homogeneous complex manifolds are considered equivalent if they are isomorphic as complex manifolds. The classification is based on methods from Lie group theory, complex analysis and algebraic geometry. Basic knowledge in these areas is presupposed.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Complex Analysis Groups & Group Theory Geometry Algebraic Geometry Topology

Survey
Survey	p. 2
The classification where G is a complex Lie group
Preparations	p. 22
The case G complex solvable	p. 28
The case G semisimple, complex	p. 38
The mixed case: Line bundles and dim[subscript C](S) ] 3	p. 51
The mixed case with [actual symbol not reproducible] and R abelian	p. 58
The mixed case with [actual symbol not reproducible] and R non-abelian	p. 70
The classification where G is a real Lie group
Preparations	p. 87
Holomorphic fibre bundles	p. 97
G solvable	p. 104
Classification for G solvable and dim[subscript R](G) = 6	p. 112
The case G solvable and dim[subscript R](G) ] 6	p. 131
The non-solvable case with R transitive	p. 148
The case dim[subscript C](G/RH) = 1	p. 162
Holomorphic fibrations in the case dim[subscript R](S) ] 3	p. 190
S-orbits in homogeneous-rational manifolds	p. 207
References	p. 225
Subject Index	p. 229
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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Paperback

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