Multiple almost Einstein structures with intersecting scale singularities (Q663341)

From the Introduction: In the current paper, we aim to characterise the \(S^l\)-doubling construction of [\textit{F. Leitner}, J. Geom. Phys. 60, No. 10, 1558--1575 (2010; Zbl 1197.53058)] exclusively by the existence of multiple almost Einstein structures with intersecting scale singularity set \(\Sigma\neq\emptyset\). This characterisation is based on a detailed analysis of the given almost Einstein structures (and the corresponding parallel standard tractors) around the scale singularity set \(\Sigma\). The discussion results in a normal form description for certain metrics in the conformal class around \(\Sigma\). The normal form description also shows the \textit{strong umbilicity} and \textit{minimality} of \(\Sigma\).