
02360916
j
2004e.04226
Bourchtein, Ludmilla
Real and complex planes and hyperplanes. (Planos e hiperplanos reais e complexos.)
Bol. Soc. Parana. Mat. (3) 21, No. 12, 137143 (2003).
2003
Sociedade Paranaense de Matem\'atica, Maring\'a
PT
I85
complex spaces
doi:10.5269/bspm.v21i12.7513
The study of the structure of ndimensional complex space $C^n$ and the different objects in this space is very important, both for analysis of properties of $C^n$ and for investigations of functions of n complex variables. In this article, real and complex planes and hyperplanes in the space $C^n$ are considered. In particular, equations for complex line and real twodimensional plane are constructed. The following statement is proved: any two distinct complex lines can have at most one common point in the space $C^n$ (n $\ge${} 2). One example shows that a similar statement is not true for two distinct real twodimensional planes in $C^n${}.