Manuscript I-B-VP-1@1 · I-B-VP-1-v1.tex · section · 6d700be9

The angular current is a smooth contraction, not singular lowering

Dilation residues and compatibility of presentations › The angular current is a smooth contraction, not singular lowering · lines 1158–1172

I-B-VP-1@1#eq:angularcontraction

Back to manuscript

The smooth contraction defining an angular scalar extension is

J_{φ}^{ext} := α^{2} R_{i} J^{i}, R_{i} = δ_{ij} R^{j} .

On $M$ , this is the actual covariant angular component, because $g_{ij} R^{i} = α^{2} R_{j}$ . Equation (eq:angularcontraction) uses a smooth polynomial multiplier on the completion; it does not multiply by the singular metric there.

Displayed formulas in this passage

I-B-VP-1@1#eq:angularcontraction · line 1161
$J_{φ}^{ext} := α^{2} R_{i} J^{i}, R_{i} = δ_{ij} R^{j} .$

Nearby in this section

proposition: Proposition: A computed contraction defect
section: The angular current is a smooth contraction, not singular lowering