complex line


Let a,bn. The set :={a+bzz} is called the complex line.

A complex line is a holomorphic complex affine imbedding of into n so that if f is holomorphic, then zf(a+bz) is also holomorphic. That is the complex structures of and n are compatible. Hence not every two dimensional real affine space is a complex line.


Let a,b1,,bkn such that b1,,bk are linearly independentMathworldPlanetmath over , then. The set


is called the complex affine space.


  • 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title complex line
Canonical name ComplexLine
Date of creation 2013-03-22 14:29:05
Last modified on 2013-03-22 14:29:05
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 5
Author jirka (4157)
Entry type Definition
Classification msc 32-00
Related topic AffineTransformation
Defines complex affine space