Manuscript XV-F-patch-ii@1 · XV-F-patch-ii.tex · section · 9674ac67

The fiber map and b 1

Patch 3: coefficient instantiation (Q3) › The fiber map and b 1 · lines 1087–1106

XV-F-patch-ii@1#eq:a1H, XV-F-patch-ii@1#eq:afrak

XIV-H writes the component pairing Hfiber

a_{1}^{α μ} [r] = A^{α μ, I} r_{I},

with $I$ ranging over symmetric index pairs, so $A$ is the coefficient matrix of XIV-H's linear fiber map $a_{1}$ ; XIV-H's definition of $a_{1}$ is in its input statement input:EC HinputEC, whose content is not in the retrieved record. XII-D displays XIIDfiber

a^{α μ, ab} = \frac{1}{2} η^{α μ} η^{ab} - η^{α (a} η^{b) μ}, a_{1}^{μν} [r] = a^{μν, ab} r_{ab}, b_{1} [r] = \frac{1}{2} η^{ab} r_{ab} .

Displayed formulas in this passage

XV-F-patch-ii@1#eq:a1H · line 1090
$a_{1}^{α μ} [r] = A^{α μ, I} r_{I},$
XV-F-patch-ii@1#eq:afrak · line 1099
$a^{α μ, ab} = \frac{1}{2} η^{α μ} η^{ab} - η^{α (a} η^{b) μ}, a_{1}^{μν} [r] = a^{μν, ab} r_{ab}, b_{1} [r] = \frac{1}{2} η^{ab} r_{ab} .$

The fiber map and b 1

Displayed formulas in this passage

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