Manuscript III-B@1 · III-B-v1.tex · section · d2c98f62

Closedness without admitting Newton tails

The supported triangular Cauchy quotient › Closedness without admitting Newton tails · lines 1198–1212

III-B@1#eq:reconstruction

For arbitrary compact metric data define

a_{0} = \frac{1}{2} N B_{00}, a_{i} = N (\partial_{j} A_{ij} - \frac{1}{2} \partial_{i} A_{j j}), b_{0} = \frac{1}{2} A_{00}, b_{i} = A_{0 i} - \partial_{i} a_{0} .

Call this auxiliary reconstruction $R (A, B)$ . It may initially be noncompact.

Displayed formulas in this passage

III-B@1#eq:reconstruction · line 1201
$a_{0} = \frac{1}{2} N B_{00}, a_{i} = N (\partial_{j} A_{ij} - \frac{1}{2} \partial_{i} A_{j j}), b_{0} = \frac{1}{2} A_{00}, b_{i} = A_{0 i} - \partial_{i} a_{0} .$