Communications in Mathematical Physics

, Volume 369, Issue 2, pp 637–673 | Cite as

Einstein Warped G2 and Spin(7) Manifolds

  • Víctor Manero
  • Luis UgarteEmail author


In this paper most of the classes of G2-structures with Einstein induced metric of negative, null, or positive scalar curvature are realized. This is carried out by means of warped G2-structures with fiber an Einstein SU(3) manifold. The torsion forms of any warped G2-structure are explicitly described in terms of the torsion forms of the SU(3)-structure and the warping function, which allows to give characterizations of the principal classes of Einstein warped G2 manifolds. Similar results are obtained for Einstein warped Spin(7) manifolds with fiber a G2 manifold.


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We are grateful to Stefan Ivanov for useful comments about Question 5.3. This work has been partially supported by the project MTM2017-85649-P (AEI/Feder, UE), and E22-17R “Algebra y Geometría” (Gobierno de Aragón/FEDER). We would like to thank the referees for their valuable suggestions and remarks that have improved the paper.


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Authors and Affiliations

  1. 1.Departamento de Matemáticas - I.U.M.A.Universidad de ZaragozaZaragozaSpain

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