Singularities of invariant connections
The authors study Schmidt's \(b\)-boundary construction [\textit{B. Schmidt}, Gen. Relativ. Gravitation 1, 269-280 (1971; Zbl 0332.53039)] for homogeneous spaces \(P/G\) with an invariant connection (\(P\) is here a Lie group, \(G\) a closed subgroup). If the connection on \(P/G\) is the reduction of an invariant connection on \(P/G\) then there are no \(b\)- incomplete inextensible curves. In the general case the authors provide examples of \(b\)-incomplete, inextensible curves and also show that different curves may have the same \(b\)-boundary point as a limit in \(\overline{P/G}\). They generalize previous work of \textit{C. T. J. Dodson} and \textit{L. J. Sulley} [Lett. Math. Phys. 1, 301 (1977)].
scientific article; zbMATH DE number 167656