Manuscript VI-B@1 · VI-B-v1.tex · section · 33798723

The prescribed cone and the supported presentation

The prescribed cone and the supported presentation · lines 228–250

VI-B@1#eq:cone

Fix

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

Prescribe

M = R_{T} \times C_{μ}^{\circ} \times R_{z}, g ˉ = - c^{2} d T^{2} + d r^{2} + α^{2} r^{2} d ϕ^{2} + d z^{2},

where $r > 0$ and $ϕ \in R / (2 π Z)$ .

The singular locus in the completion is

W = R_{T} \times {o} \times R_{z} .

It is a worldsheet. No smooth metric chart or ordinary pointwise Einstein tensor is asserted on $W$ .

Displayed formulas in this passage

VI-B@1#eq:cone · line 237
$M = R_{T} \times C_{μ}^{\circ} \times R_{z}, g ˉ = - c^{2} d T^{2} + d r^{2} + α^{2} r^{2} d ϕ^{2} + d z^{2},$
unlabeled · line 232
$c > 0, 0 < μ < 2 π, α = 1 - \frac{μ}{2 π} .$
unlabeled · line 245
$W = R_{T} \times {o} \times R_{z} .$