Conformal mapping

Japanese: 等角写像 - とうかくしゃぞう

When a mapping f from one space M to another space N is one-to-one continuous and the angle between two differentiable curves C ₁ and C ₂ in M is always equal to the angle between f(C ₁ ) and f(C ₂ ) in N, f is called a conformal mapping. In particular, if M and N are complex planes (with (x, y) and (u, v) being Cartesian coordinates) representing the complex numbers z = x + iy and w = u + iv, respectively, the holomorphic function (function theory) z = f(w) gives a conformal mapping. It is applied to the mathematical theory of potentials and wings.
→ Related topics Mapping | Riemann

Source : Heibonsha Encyclopedia About MyPedia Information

Japanese:

一つの空間Mから他の空間Nへの写像fが一対一連続で，Mの二つの微分可能曲線C₁，C₂のなす角が常にNでf（C₁），f（C₂）のなす角に等しいとき，fを等角写像という。特にM，Nがそれぞれ複素数z＝x＋iy，w＝u＋ivを表す複素平面（（x，y），（u，v）を直交座標とする）であれば，正則関数（関数論）z＝f（w）は等角写像を与える。ポテンシャルや翼の数学的理論に応用される。
→関連項目写像｜リーマン

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