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An even Clifford diamond

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Abstract

We present a diamond shaped diagram for even Clifford manifolds similar to the quaternion-Kähler diamond studied by Ch. Boyer and K. Galicki. We define two spaces \({\mathcal {S}}\) and \({\mathcal {U}}\) which fiber over an even Clifford manifold which, together with the twistor space \({\mathcal {Z}}\) defined by G. Arizmendi and Ch. Hadfield, form a diamond shaped diagram of fibrations. Moreover, we prove that, under certain natural conditions, \({\mathcal {Z}}\) is Kahler–Einstein, \({\mathcal {S}}\) is Sasaki–Einstein and \({\mathcal {U}}\) is special-Kähler.

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Authors and Affiliations

  1. Department of Actuarial Sciences, Physics and Mathematics, UDLAP, San Andrés Cholula, Puebla, Mexico

    Gerardo Arizmendi

  2. Centro de Investigación en Matemáticas, A. P. 402, C.P. 36000, Guanajuato, Gto, Mexico

    Rafael Herrera

  3. Dipartimento di Matematica, Sapienza Università di Roma, piazzale Aldo Moro 2, 00185, Rome, Italy

    Paolo Piccinni

Authors
  1. Gerardo Arizmendi
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  2. Rafael Herrera
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  3. Paolo Piccinni
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Correspondence to Gerardo Arizmendi.

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G. Arizmendi: Partially supported by a CONACyT grant. R. Herrera: Partially supported CONACyT-Mexico and INdAM-Italy grants. P. Piccinni: Partially supported by INdAM-GNSAGA, by the MIUR-PRIN 2017 grant “Real and Complex Manifolds”, and by the Sapienza Università di Roma grant “Identità polinomiali e metodi combinatori in strutture algebriche e geometriche”.

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Arizmendi, G., Herrera, R. & Piccinni, P. An even Clifford diamond. Ann Glob Anal Geom 57, 465–487 (2020). https://doi.org/10.1007/s10455-020-09709-6

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