conformalFactorAt — Mathlib

English

If h is conformal at x, then there exists c > 0 with the inner-product relation as above.

Русский

Если h конформно в точке x, существует c > 0 с указанным relation между скалярными произведениями.

LaTeX

$$$ \exists c>0, \forall u,v, \langle f'(x)u, f'(x)v \rangle = c \langle u,v \rangle $$$

Lean4

/-- The conformal factor of a conformal map at some point `x`. Some authors refer to this function
as the characteristic function of the conformal map. -/
def conformalFactorAt {f : E → F} {x : E} (h : ConformalAt f x) : ℝ :=
  Classical.choose (conformalAt_iff'.mp h)

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