Noncompact Riemannian spaces with the holonomy group spin(7) and 3-Sasakian manifolds

1. Ya. V. Bazaikin, “On the New Examples of Complete Noncompact Spin(7)-Holonomy Metrics,” Sib. Mat. Zh. 48(1), 11–32 (2007) [Sib. Math. J. 48, 8–25 (2007)].

   MATH  MathSciNet  Google Scholar 

2. R. L. Bryant, “Metrics with Exceptional Holonomy,” Ann. Math. 126, 525–576 (1987).

   Article  Google Scholar 

3. R. L. Bryant and S. L. Salamon, “On the Construction of Some Complete Metrics with Exceptional Holonomy,” Duke Math. J. 58, 829–850 (1989).

   Article  MATH  MathSciNet  Google Scholar 

4. D. D. Joyce, “Compact 8-Manifolds with Holonomy Spin(7),” Invent. Math. 123(3), 507–552 (1996).

   Article  MATH  MathSciNet  Google Scholar 

5. M. Cvetič, G. W. Gibbons, H. Lü, and C. N. Pope, “New Complete Non-compact Spin(7) Manifolds,” Nucl. Phys. B 620, 29–54 (2002).

   Article  MATH  Google Scholar 

6. M. Cvetič, G. W. Gibbons, H. Lü, and C. N. Pope, “New Cohomogeneity One Metrics with Spin(7) Holonomy,” J. Geom. Phys. 49, 350–365 (2004).

   Article  MATH  MathSciNet  Google Scholar 

7. M. Cvetič, G. W. Gibbons, H. Lü, and C. N. Pope, “Cohomogeneity One Manifolds of Spin(7) and G ₂ Holonomy,” Phys. Rev. D 65(10), 106004 (2002).

   Google Scholar 

8. S. Gukov and J. Sparks, “M-Theory on Spin(7) Manifolds,” Nucl. Phys. B 625, 3–69 (2002).

   Article  MATH  MathSciNet  Google Scholar 

9. H. Kanno and Y. Yasui, “On Spin(7) Holonomy Metric Based on SU(3)/U(1),” J. Geom. Phys. 43, 293–309 (2002).

   Article  MATH  MathSciNet  Google Scholar 

10. H. Kanno and Y. Yasui, “On Spin(7) Holonomy Metric Based on SU(3)/U(1). II,” J. Geom. Phys. 43, 310–326 (2002).

    Article  MATH  MathSciNet  Google Scholar 

11. A. Gray, “Weak Holonomy Groups,” Math. Z. 123, 290–300 (1971).

    Article  MATH  MathSciNet  Google Scholar 

12. C. Boyer and K. Galicki, “3-Sasakian Manifolds,” in Surveys in Differential Geometry: Essays on Einstein Manifolds (International Press, Boston, MA, 1999), Surv. Diff. Geom. 6, pp. 123–184.

    Google Scholar 

13. F. Reidegeld, “Spin(7)-Manifolds of Cohomogeneity One,” in Special Geometries in Mathematical Physics: Workshop, Kuehlungsborn, 2008 (in press).

14. L. Bérard-Bergery, “Sur de nouvelles variétés riemanniennes d’Einstein,” Inst. Élie Cartan, Univ. Nancy 6, 1–60 (1982).

    Google Scholar 

15. D. N. Page and C. N. Pope, “Inhomogeneous Einstein Metrics on Complex Line Bundles,” Class. Quantum Grav. 4(2), 213–225 (1987).

    Article  MATH  MathSciNet  Google Scholar 

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