On the construction of some complete metrics with exceptional holonomy
Until the first author's recent paper [Ann. Math., II. Ser. 126, 525-576 (1987; Zbl 0637.53042)], the two Lie groups \(G_ 2\) and Spin(7) were the only two members of \textit{M. Berger}'s list of holonomy groups of irreducible Riemannian manifolds [Bull. Soc. Math. Fr. 83, 279-330 (1955; Zbl 0068.36002)] whose existence was in doubt. The present paper improves upon the above by providing explicit construction of three distinct complete Riemannian metrics whose holonomy group is \(G_ 2\), one complete metric whose holonomy group is Spin(7), and various other incomplete metrics with exceptional holonomy. The construction techniques may be of interest to those studying Ricci flat and Einstein spaces.
scientific article; zbMATH DE number 4115451
scientific article