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

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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.

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References

  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).

  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).

    Article  MathSciNet  MATH  Google Scholar 

  3. Brandhuber A., “G 2 holonomy spaces from invariant three-forms,” Nucl. Phys. B, 629, No. 1–3, 393–416 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  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).

    MathSciNet  MATH  Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

  7. Bazaĭkin Ya. V., “On the new examples of complete noncompact Spin(7)-holonomy metrics,” Siberian Math. J., 48, No. 1, 8–25 (2007).

    Article  MathSciNet  Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    O. A. Bogoyavlenskaya

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  1. O. A. Bogoyavlenskaya
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Correspondence to O. A. Bogoyavlenskaya.

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Original Russian Text Copyright © 2013 Bogoyavlenskaya O.A.

The author was supported by the Russian Foundation for Basic Research (Grant 12-01-00124-a), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-544.2012.1), and the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” for 2009–2013 (State Contract 8206 on 06.08.2012).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 3, pp. 551–562, May–June, 2013.

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Bogoyavlenskaya, O.A. On a new family of complete G 2-holonomy Riemannian metrics on S 3 × ℝ4 . Sib Math J 54, 431–440 (2013). https://doi.org/10.1134/S0037446613030075

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  • DOI: https://doi.org/10.1134/S0037446613030075

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