Manuscript XXII-E@1 · XXII-E.tex · definition · 51c99d2f

Definition: Second metric jet

A well-defined linearized comparison › Finite-dimensional metric jets · lines 659–676

XXII-E@1#def:jet

At a declared formal marked point of the affine comparison carrier, set

J^{2} = Sym^{2} (V_{D}^{*}) \otimes (R \oplus V_{D}^{*} \oplus Sym^{2} (V_{D}^{*})) .

A jet $j \in J^{2}$ has components

(h_{μν}, h_{μν ∣ α}, h_{μν ∣ α β}),

symmetric in $μ, ν$ and in $α, β$ . The vertical bar denotes a formal derivative slot, not a derivative already measured in the process data.

Displayed formulas in this passage

unlabeled · line 663
$J^{2} = Sym^{2} (V_{D}^{*}) \otimes (R \oplus V_{D}^{*} \oplus Sym^{2} (V_{D}^{*})) .$
unlabeled · line 670
$(h_{μν}, h_{μν ∣ α}, h_{μν ∣ α β}),$