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Siberian Mathematical Journal

, Volume 54, Issue 3, pp 431–440 | Cite as

On a new family of complete G 2-holonomy Riemannian metrics on S 3 × ℝ4

  • O. A. BogoyavlenskayaEmail author
Article
  • 71 Downloads

Abstract

Studying a system of first-order nonlinear ordinary differential equations for the functions determining a deformation of the standard conic metric over S 3 × S 3, we prove the existence of a one-parameter family of complete G 2-holonomy Riemannian metrics on S 3 × ℝ4.

Keywords

special holonomy groups asymptotically locally conic Riemannian metrics 

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References

  1. 1.
    Bazaĭkin Ya. V. and Bogoyavlenskaya O. A., “Complete G 2-holonomy Riemannian metrics on cone deformations over S 3 × S 3,” Math. Notes (to be published).Google Scholar
  2. 2.
    Brandhuber A., Gomis J., Gubser S. S., and Gukov S., “Gauge theory at large N and new G 2 holonomy metrics,” Nucl. Phys. B, 611, No. 1–3, 179–204 (2001).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Brandhuber A., “G 2 holonomy spaces from invariant three-forms,” Nucl. Phys. B, 629, No. 1–3, 393–416 (2002).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Cvetic M., Gibbons G. W., Lu H., and Pope C. N., “A G 2 unification of the deformed and resolved conifolds,” Phys. Lett. B, 534, No. 1–4, 172–180 (2002).MathSciNetzbMATHGoogle Scholar
  5. 5.
    Chong Z. W., Cvetic M., Gibbons G. W., Lu H., Pope C. N., and Wagner P., “General metrics of G 2 holonomy and contraction limits,” Nucl. Phys. B, 638, No. 3, 459–482 (2002).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Bryant R. L. and Salamon S. L., “On the construction of some complete metrics with exceptional holonomy,” Duke Math. J., 58, No. 3, 829–850 (1989).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Bazaĭkin Ya. V., “On the new examples of complete noncompact Spin(7)-holonomy metrics,” Siberian Math. J., 48, No. 1, 8–25 (2007).MathSciNetCrossRefGoogle Scholar
  8. 8.
    Gibbons G. W., Page D. N., and Pope C. N., “Einstein metrics on S 3, ℝ3, and ℝ4 bundles,” Comm. Math. Phys., 127, No. 3, 529–553 (1990).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia

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