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Sibirsk. Mat. Zh., 2007, Volume 48, Number 1, Pages 11–32 (Mi smj2)  

This article is cited in 16 scientific papers (total in 16 papers)

On the new examples of complete noncompact Spin(7)-holonomy metrics

Ya. V. Bazaikin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We construct some complete Spin(7)-holonomy Riemannian metrics on the noncompact orbifolds that are $\mathbb R^4$-bundles with an arbitrary 3-Sasakian spherical fiber $M$. We prove the existence of the smooth metrics for $M=S^7$ and $M=SU(3)/U(1)$ which were found earlier only numerically.

Keywords: exceptional holonomy groups, 3-Sasakian manifold.

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English version:
Siberian Mathematical Journal, 2007, 48:1, 8–25

Bibliographic databases:

UDC: 514.763.3
Received: 20.02.2006

Citation: Ya. V. Bazaikin, “On the new examples of complete noncompact Spin(7)-holonomy metrics”, Sibirsk. Mat. Zh., 48:1 (2007), 11–32; Siberian Math. J., 48:1 (2007), 8–25

Citation in format AMSBIB
\by Ya.~V.~Bazaikin
\paper On the new examples of complete noncompact Spin(7)-holonomy metrics
\jour Sibirsk. Mat. Zh.
\yr 2007
\vol 48
\issue 1
\pages 11--32
\jour Siberian Math. J.
\yr 2007
\vol 48
\issue 1
\pages 8--25

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    This publication is cited in the following articles:
    1. Ya. V. Bazaikin, E. G. Malkovich, “$G_2$-holonomy metrics connected with a 3-Sasakian manifold”, Siberian Math. J., 49:1 (2008), 1–4  mathnet  crossref  mathscinet  zmath  isi
    2. Ya. V. Bazaikin, “Noncompact Riemannian Spaces with the Holonomy Group $\operatorname{Spin}(7)$ and 3-Sasakian Manifolds”, Proc. Steklov Inst. Math., 263 (2008), 2–12  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. Reidegeld F., “Special cohomogeneity-one metrics with Q(1,1,1) or M-1,M-1,M-0 as the principal orbit”, J Geom Phys, 60:9 (2010), 1069–1088  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Ya. V. Bazaǐkin, I. V. Matvienko, “On the moment-angle manifolds of positive Ricci curvature”, Siberian Math. J., 52:1 (2011), 11–22  mathnet  crossref  mathscinet  isi
    5. E. G. Malkovich, “On new explicit Riemannian $SU(2(n+1))$-holonomy metrics”, Siberian Math. J., 52:1 (2011), 74–77  mathnet  crossref  mathscinet  isi
    6. Ya. V. Bazaikin, E. G. Malkovich, “$\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group $\mathrm{SU}(4)$”, Sb. Math., 202:4 (2011), 467–493  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Reidegeld F., “Exceptional holonomy and Einstein metrics constructed from Aloff-Wallach spaces”, Proc London Math Soc, 102:6 (2011), 1127–1160  crossref  mathscinet  zmath  isi  elib  scopus
    8. Bazaikin Ya.V., “Spetsialnye gruppy golonomii rimanovykh prostranstv”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 93–105  elib
    9. 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
    10. O. A. Bogoyavlenskaya, “On a new family of complete $G_2$-holonomy Riemannian metrics on $S^3\times\mathbb R^4$”, Siberian Math. J., 54:3 (2013), 431–440  mathnet  crossref  mathscinet  isi
    11. de Andres L.C., Fernandez M., Ivanov S., Santisteban J.A., Ugarte L., Vassilev D., “Quaternionic Kahler and Spin(7) Metrics Arising From Quaternionic Contact Einstein Structures”, Ann. Mat. Pura Appl., 193:1 (2014), 261–290  crossref  mathscinet  zmath  isi  scopus
    12. Malkovich E.G., “Noncompact Riemannian Spaces With G (2), Spin(7) and Su(2M) Holonomies”, Phys. Part. Nuclei, 45:3 (2014), 550–567  crossref  isi  elib  scopus
    13. A. S. Galaev, “Holonomy groups of Lorentzian manifolds”, Russian Math. Surveys, 70:2 (2015), 249–298  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    14. 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
    15. Reidegeld F., “Exceptional Holonomy on Vector Bundles With Two-Dimensional Fibers”, J. Geom. Anal., 25:1 (2015), 281–297  crossref  mathscinet  zmath  isi  scopus
    16. E. G. Malkovich, “Dirac flow on the $3$-sphere”, Siberian Math. J., 57:2 (2016), 340–351  mathnet  crossref  crossref  mathscinet  isi  elib
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