Planos e hiperplanos reais e complexos

Ludmila Bourchtein

doi:10.5269/bspm.v21i1-2.7513

Abstract

The study of the structure of n-dimensional 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 two-dimensional 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/geq2). One example show that a similar statement is not true for two distinct real two-dimensional planes in C^n.

Highlights

Ludmila Bourchtein abstract: The study of the structure of n-dimensional complex space Cn and the different objects in this space is very important, both for analysis of properties of Cn and for investigations of functions of n complex variables
The following statement is proved: any two distinct complex lines can have at most one common point in the space Cn(n/geq2)
One example show that a similar statement is not true for two distinct real two-dimensional planes in Cn

Summary

Introduction

Ludmila Bourchtein abstract: The study of the structure of n-dimensional complex space Cn and the different objects in this space is very important, both for analysis of properties of Cn and for investigations of functions of n complex variables. 2. Planos complexos em Cn. Equacao da reta complexa. 1, istoe, k = n−1; a reta complexa se define para o conjunto de n − 1 vetores aj ∈ Cn, j = 1, ..., n − 1 linearmente independentes sobre o corpo C; isto significa que da igualdade λ1a1 + λ2a2 + ...

Results

Conclusion