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

Abstract

We construct some complete Spin(7)-holonomy Riemannian metrics on the noncompact orbifolds that are ℝ4-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.

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Original Russian Text Copyright © 2007 Bazaĭkin Ya. V.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 1, pp. 11–32, January–February, 2007.

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Bazaikin, Y.V. On the new examples of complete noncompact Spin(7)-holonomy metrics. Sib Math J 48, 8–25 (2007). https://doi.org/10.1007/s11202-007-0003-7

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Keywords

  • exceptional holonomy groups
  • 3-Sasakian manifold