Manuscript I-B-G@2 · I-B-G-v2.tex · definition · 3b4d700f

Definition: Angularly small chart

Supported replacement of flat-completion operators › The geometric arrival window · lines 1630–1648

I-B-G@2#def:chart

An angularly small developing chart is an open $U \subset M$ contained in

{r > r_{U}, φ \in I}, r_{U} > 0, ∣ I ∣ < π,

with a fixed angular lift on $I$ , and equipped with the developing map of Section sec:host. For its spatial points,

∣ α (φ - φ^{'}) ∣ < π α, ∣ dev_{sp} x - dev_{sp} x^{'} ∣ = R_{0} = d (x, x^{'}) .

The bundle is trivialised by a local parallel frame.

Displayed formulas in this passage

unlabeled · line 1634
${r > r_{U}, φ \in I}, r_{U} > 0, ∣ I ∣ < π,$
unlabeled · line 1641
$∣ α (φ - φ^{'}) ∣ < π α, ∣ dev_{sp} x - dev_{sp} x^{'} ∣ = R_{0} = d (x, x^{'}) .$