Manuscript IV-B@1 · IV-B-v1.tex · section · dfb66408

Conical product, signature, and rods

The prescribed geometry and the completion boundary › Conical product, signature, and rods · lines 224–243

IV-B@1#eq:metric

Fix

0 < μ < 2 π, α = 1 - \frac{μ}{2 π}, c > 0.

Let

C_{μ}^{\circ} = (0, \infty) \times (R /2 π Z), M = R_{T} \times C_{μ}^{\circ} \times R_{z},

and prescribe

g = - c^{2} d T^{2} + d r^{2} + α^{2} r^{2} d ϕ^{2} + d z^{2} .

The time orientation is that of $\partial_{T}$ .

Displayed formulas in this passage

IV-B@1#eq:metric · line 238
$g = - c^{2} d T^{2} + d r^{2} + α^{2} r^{2} d ϕ^{2} + d z^{2} .$
unlabeled · line 227
$0 < μ < 2 π, α = 1 - \frac{μ}{2 π}, c > 0.$
unlabeled · line 232
$C_{μ}^{\circ} = (0, \infty) \times (R /2 π Z), M = R_{T} \times C_{μ}^{\circ} \times R_{z},$