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Einstein Warped G2 and Spin(7) Manifolds

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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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Acknowledgements

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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  1. Departamento de Matemáticas - I.U.M.A., Universidad de Zaragoza, Campus Plaza San Francisco, 50009, Zaragoza, Spain

    Víctor Manero & Luis Ugarte

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  1. Víctor Manero
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  2. Luis Ugarte
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Correspondence to Luis Ugarte.

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Communicated by P. Chrusciel

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Manero, V., Ugarte, L. Einstein Warped G2 and Spin(7) Manifolds. Commun. Math. Phys. 369, 637–673 (2019). https://doi.org/10.1007/s00220-019-03355-1

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