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Einstein metrics onS 3,R 3 andR 4 bundles

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Abstract

Starting from a 4n-dimensional quaternionic Kähler base space, we construct metrics of cohomogeneity one in (4n+3) dimensions whose level surfaces are theS 2 bundle space of almost complex structures on the base manifold. We derive the conditions on the metric functions that follow from imposing the Einstein equation, and obtain solutions both for compact and non-compact (4n+3)-dimensional spaces. Included in the non-compact solutions are two Ricci-flat 7-dimensional metrics withG 2 holonomy. We also discuss two other Ricci-flat solutions, one on theR 4 bundle overS 3 and the other on anR 4 bundle overS 4. These haveG 2 and Spin(7) holonomy respectively.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, CB3 9EW, Cambridge, UK

    G. W. Gibbons

  2. Department of Physics, The Pennsylvania State University, 16802, University Park, PA, USA

    D. N. Page

  3. Center for Theoretical Physics, Department of Physics, Texas A&M University, 77843, College Station, TX, USA

    C. N. Pope

Authors
  1. G. W. Gibbons
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  2. D. N. Page
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  3. C. N. Pope
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Communicated by L. Alvarez-Gaumé

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Gibbons, G.W., Page, D.N. & Pope, C.N. Einstein metrics onS 3,R 3 andR 4 bundles. Commun.Math. Phys. 127, 529–553 (1990). https://doi.org/10.1007/BF02104500

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  • DOI: https://doi.org/10.1007/BF02104500

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