Theorems · Theorem · geometry

Orientation.kahler_rotation_left

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
  (o : Orientation ℝ V (Fin 2)) (x y : V) (θ : Real.Angle),
  (o.kahler ((o.rotation θ) x)) y = (starRingEnd ℂ) ↑θ.toCircle * (o.kahler x) y

Rotating the first of two vectors by θ scales their Kähler form by cos θ - sin θ * I.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation

Cited by

1 results in Mathlib

Foundations

Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact