Abstract:
A system of differential equations with 5 unknowns is fully investigated; this system is equivalent to the existence of a parallel 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, SU(4), which generalize Calabi's metrics.
Bibliography: 10 titles.
Citation:
Ya. V. Bazaikin, E. G. Malkovich, “Spin(7)-structures on complex linear bundles and explicit Riemannian metrics with holonomy group
SU(4)”, Sb. Math., 202:4 (2011), 467–493
\Bibitem{BazMal11}
\by Ya.~V.~Bazaikin, E.~G.~Malkovich
\paper $\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group
$\mathrm{SU}(4)$
\jour Sb. Math.
\yr 2011
\vol 202
\issue 4
\pages 467--493
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Linking options:
https://www.mathnet.ru/eng/sm7657
https://doi.org/10.1070/SM2011v202n04ABEH004152
https://www.mathnet.ru/eng/sm/v202/i4/p3
This publication is cited in the following 8 articles:
E. G. Malkovich, “Dirac flow on the 3-sphere”, Siberian Math. J., 57:2 (2016), 340–351
F. Reidegeld, “Exceptional holonomy on vector bundles with two-dimensional fibers”, J. Geom. Anal., 25:1 (2015), 281–297
O. A. Bogoyavlenskaya, “O deformatsiyakh metrik s gruppoi golonomii Spin(3,4) na konusakh nad psevdo-rimanovymi mnogoobraziyami”, Sib. elektron. matem. izv., 12 (2015), 940–946
E. G. Malkovich, “Noncompact Riemannian spaces with G2, Spin(7) and SU(2m) holonomies”, Phys. Part. Nuclei, 45:3 (2014), 550–567
Ya. V. Bazaikin, O. A. Bogojavlenskaja, “Complete Riemannian Metrics with Holonomy Group G2 on Deformations of Cones over S3×S3”, Math. Notes, 93:5 (2013), 643–653
Citation in format AMSBIB
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