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Sbornik: Mathematics, 2011, Volume 202, Issue 4, Pages 467–493
DOI: https://doi.org/10.1070/SM2011v202n04ABEH004152 (Mi sm7657) 		 
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
English version PDF (430 kB) Citations (8)
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DOI: https://doi.org/10.1070/SM2011v202n04ABEH004152
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.
Received: 20.11.2009 and 11.06.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 4, Pages 3–30
DOI: https://doi.org/10.4213/sm7657
Bibliographic databases:
Document Type: Article
UDC: 514.763.3
MSC: 53C25, 53C29
Language: English
Original paper language: Russian
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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  • https://www.mathnet.ru/eng/sm/v202/i4/p3
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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