Noncompact Riemannian spaces with the holonomy group spin\((7)\) and 3-Sasakian manifolds (Q735616)

The author considers the existence of Riemannian metrics having the special holonomy group \(\text{Spin}(7)\) which smoothly resolve the standard cone metrics on non-compact manifolds and orbifolds related to 7-dimensional 3-Sasakian spaces. This completes his study began in [Sib. Mat. Zh. 48, No.~1, 11--32 (2007); translation in Sib. Math. J. 48, No.~1, 8--25 (2007; Zbl 1164.53360)]. Contents include: Introduction and main results (which contains an overview of the topic); Construction of \(\text{Spin}(7)\)-holonomy metrics; \(\text{Spin}(7)\)-holonomy metrics on \({\mathcal M}_1\); and References.