Painlevé expansions, cohomogeneity one metrics and exceptional holonomy
The authors continue their study of ordinary differential equations arising as reductions of the Einstein equations [J. Reine Angew. Math. 524, 97--128 (2000; Zbl 0988.53018), Commun. Math. Phys. 208, 225--243 (1999; Zbl 0958.83007), J. Geom. Phys. 38, No. 3--4, 183--206 (2001; Zbl 0987.53017), ibid. 48, No. 1, 12--43 (2003; Zbl 1029.83005)]. The article at hand concentrates on general results about the Painlevé analysis of the cohomogeneity 1 Ricci-flat equations in the situation when the isotropy representation of the principal orbit consists of pairwise inequivalent representations and examples. The paper [J. Math. Phys. 44, No. 8, 3383--3406 (2003; Zbl 1062.37053)] is a sequel to the present one, where the principal orbits are the Aloff-Wallach spaces and certain principal circle bundles over a product of two Fano varieties.
scientific article; zbMATH DE number 2148047