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Manuscript VIII-ST@1 · VIII-ST.tex · section · fe979f3b

Packet and chart conventions

Lorentz-affine matching and complete certificates › Packet and chart conventions · lines 844–862

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For a Cartesian face gradient $g$ , $∣ g ∣ < 1$ , let

B (g) = (γ - γ g - γ g^{T} I_{2} + (γ - 1) g g^{T} / ∣ g ∣^{2}), γ = (1 - ∣ g ∣^{2})^{- 1/2},

with $B (0) = I$ . For a face $τ = q + g \cdot x$ , choose the ambient affine chart

A_{f} (y) = B (g) y - γ q t,

and extend it by the identity on $ζ$ . Resting faces may instead use the ambient identity chart.

Displayed formulas in this passage

unlabeled · line 847
$B (g) = (γ - γ g - γ g^{T} I_{2} + (γ - 1) g g^{T} / ∣ g ∣^{2}), γ = (1 - ∣ g ∣^{2})^{- 1/2},$
unlabeled · line 857
$A_{f} (y) = B (g) y - γ q t,$

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