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Twistor spaces of Riemannian manifolds with even Clifford structures

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Abstract

In this paper, we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak-\(\mathrm {Spin}(9)\) structures. We also construct almost complex structures on the twistor space for parallel even Clifford structures and check their integrability. Moreover, we prove that in some cases one can give Kähler and nearly Kähler metrics to these spaces.

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Acknowledgments

The first author would like to thank Rafael Herrera for his encouragement and comments and Andrei Moroianu for useful discussions and hospitality during a visit to Université de Versailles-St Quentin. The second author would also like to thank Andrei Moroianu for valued guidance of his Masters during which part of this work was completed. The first author was partially supported by CONACyT scholarship and the second author by a PGSM International scholarship.

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Correspondence to Gerardo Arizmendi.

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Arizmendi, G., Hadfield, C. Twistor spaces of Riemannian manifolds with even Clifford structures. Ann Glob Anal Geom 51, 11–20 (2017). https://doi.org/10.1007/s10455-016-9520-6

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  • DOI: https://doi.org/10.1007/s10455-016-9520-6

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