Geodesic
$\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group
Sbornik. Mathematics, Tome 202 (2011) no. 4, pp. 467-493 Cet article a éte moissonné depuis la source Math-Net.Ru

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A system of differential equations with 5 unknowns is fully investigated; this system is equivalent to the existence of a parallel $\mathrm{Spin}(7)$-structure on a cone over a 3-Sasakian manifold. A continuous one-parameter family of solutions to this system is explicitly constructed; it corresponds to metrics with a special holonomy group, $\mathrm{SU}(4)$, which generalize Calabi's metrics. Bibliography: 10 titles.
Keywords: holonomy group, 3-Sasakian manifold. 
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Ya. V. Bazaikin; E. G. Malkovich. $\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group. Sbornik. Mathematics, Tome 202 (2011) no. 4, pp. 467-493. http://geodesic.mathdoc.fr/item/SM_2011_202_4_a0/

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