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Mat. Sb., 2011, Volume 202, Number 4, Pages 3–30 (Mi msb7657)  

This article is cited in 8 scientific papers (total in 8 papers)

$\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group $\mathrm{SU}(4)$

Ya. V. Bazaikina, E. G. Malkovichb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University

Abstract: 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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7657

Full text: PDF file (617 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2011, 202:4, 467–493

Bibliographic databases:

UDC: 514.763.3
MSC: 53C25, 53C29
Received: 20.11.2009 and 11.06.2010

Citation: Ya. V. Bazaikin, E. G. Malkovich, “$\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group $\mathrm{SU}(4)$”, Mat. Sb., 202:4 (2011), 3–30; Sb. Math., 202:4 (2011), 467–493

Citation in format AMSBIB
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\by Ya.~V.~Bazaikin, E.~G.~Malkovich
\paper $\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group
$\mathrm{SU}(4)$
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\yr 2011
\vol 202
\issue 4
\pages 467--493
\crossref{https://doi.org/10.1070/SM2011v202n04ABEH004152}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959832968}


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  • https://doi.org/10.4213/sm7657
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Malkovich E.G., “Potok dlya Spin(7)-struktury”, Vestn. Kemerovskogo gos. un-ta, 2011, no. 3/1, 147–150  elib
    2. Bazaikin Ya.V., “Spetsialnye gruppy golonomii rimanovykh prostranstv”, Vestn. Kemerovskogo gos. un-ta, 2011, no. 3/1, 93–105  elib
    3. Ya. V. Bazaikin, O. A. Bogojavlenskaja, “Complete Riemannian Metrics with Holonomy Group $G_2$ on Deformations of Cones over $S^3\times S^3$”, Math. Notes, 93:5 (2013), 643–653  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Conlon R.J., Hein H.-J., “Asymptotically conical Calabi-Yau manifolds, I”, Duke Math. J., 162:15 (2013), 2855–2902  crossref  mathscinet  zmath  isi  scopus
    5. E. G. Malkovich, “Noncompact Riemannian spaces with $G_2$, $Spin(7)$ and $SU(2m)$ holonomies”, Phys. Part. Nuclei, 45:3 (2014), 550–567  crossref  isi  elib  scopus
    6. F. Reidegeld, “Exceptional holonomy on vector bundles with two-dimensional fibers”, J. Geom. Anal., 25:1 (2015), 281–297  crossref  mathscinet  zmath  isi  scopus
    7. 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  mathnet  crossref
    8. E. G. Malkovich, “Dirac flow on the $3$-sphere”, Siberian Math. J., 57:2 (2016), 340–351  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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