Manuscript Em01-F@3 · Em01-F-v3.tex · section · 225e59af

Exact characteristic coordinates

Tensor conventions and separated characteristic geometry › Exact characteristic coordinates · lines 503–525

Em01-F@3#eq:coordinates

Set

ℓ_{n} = (1, n), k_{n} = (1, - n), ∣ n ∣ = 1,

and choose a smooth orthonormal transverse frame $E_{A} = (0, e_{A})$ , $A = 1, 2$ , on a sphere subchart. Use

z b y = a + r, = a + β ℓ_{n} + u k_{n}, = a + α ℓ_{n} + v k_{n} + ξ^{A} E_{A} .

There are eight tangential coordinates $(a, n, α, β)$ and eight normal coordinates $(r, u, v, ξ)$ .

Displayed formulas in this passage

Em01-F@3#eq:coordinates · line 513
$z b y = a + r, = a + β ℓ_{n} + u k_{n}, = a + α ℓ_{n} + v k_{n} + ξ^{A} E_{A} .$
unlabeled · line 506
$ℓ_{n} = (1, n), k_{n} = (1, - n), ∣ n ∣ = 1,$