Manuscript VII-E-ST@1 · VII-E-ST.tex · section · d28d9c5d

Prescribed conical geometry and supported presentation

Prescribed conical geometry and supported presentation · lines 225–245

VII-E-ST@1#eq:cone

Fix

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

The physical smooth background is

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 $ϕ$ is periodic with period $2 π$ . Its completion has the conical worldsheet

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

No smooth Einstein tensor is assigned on $W$ .

Displayed formulas in this passage

VII-E-ST@1#eq:cone · line 234
$M = R_{T} \times C_{μ}^{\circ} \times R_{z}, g ˉ = - c^{2} d T^{2} + d r^{2} + α^{2} r^{2} d ϕ^{2} + d z^{2},$
unlabeled · line 229
$c > 0, 0 < μ < 2 π, α = 1 - \frac{μ}{2 π} .$
unlabeled · line 241
$W = R_{T} \times {o} \times R_{z} .$