# example of conformal mapping

Consider the four curves $A=\{t\}$, $B=\{t+it\}$, $C=\{it\}$ and $D=\{-t+it\}$, $t\in [-10,10]$. Suppose there is a mapping $f:\u2102\mapsto \u2102$ which maps $A$ to $D$ and $B$ to $C$. Is $f$ conformal at ${z}_{0}=0$? The size of the angles between $A$ and $B$ at the point of intersection ${z}_{0}=0$ is preserved, however the orientation is not. Therefore $f$ is not conformal at ${z}_{0}=0$. Now suppose there is a function^{} $g:\u2102\mapsto \u2102$ which maps $A$ to $C$ and $B$ to $D$. In this case we see not only that the size of the angles is preserved, but also the orientation. Therefore $g$ is conformal at ${z}_{0}=0$.

Title | example of conformal mapping^{} |
---|---|

Canonical name | ExampleOfConformalMapping |

Date of creation | 2013-03-22 13:36:36 |

Last modified on | 2013-03-22 13:36:36 |

Owner | Johan (1032) |

Last modified by | Johan (1032) |

Numerical id | 6 |

Author | Johan (1032) |

Entry type | Example |

Classification | msc 30E20 |

Related topic | CategoryOfRiemannianManifolds |