Manuscript III@2 · III.tex · section · 82dad3e5

The coupled jet

The coupled first-order jet and retarded harmonic section › The coupled jet · lines 1222–1241

III@2#eq:jet-section

There is no spacelike-compact requirement on $h$ in this definition. Its harmonic part may be noncompact. The retarded prescription needs the condition on $D h$ . The scalar forcing remains spacelike compact because its support is contained in that of $ϕ_{0}$ .

Set

S_{R} (h, ϕ_{0}, ϕ_{1}) = (Π_{R} h, ϕ_{0}, ϕ_{1} - X_{w_{R} (h)} ϕ_{0}) .

Displayed formulas in this passage

III@2#eq:jet-section · line 1231
$S_{R} (h, ϕ_{0}, ϕ_{1}) = (Π_{R} h, ϕ_{0}, ϕ_{1} - X_{w_{R} (h)} ϕ_{0}) .$

Nearby in this section

definition: Definition: Coupled first-order jet
theorem: Theorem: Unique retarded harmonic section
figure: Unique retarded harmonic representative
lemma: Lemma: Nonempty scalar fibers