• Twistor space of a generalized quaternionic manifold

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    • Keywords


      Generalized geometries; twistor theory; differential-geometric methods; hyper-Kähler and quaternionic Kähler geometry; special geometry.

    • Abstract


      We first make a little survey of the twistor theory for hypercomplex, generalized hypercomplex, quaternionic or generalized quaternionic manifolds. This last theory was initiated by Pantilie (Ann. Mat. Pura. Appl. 193 (2014) 633–641), and allows one to extend the Penrose correspondence from the quaternion to the generalized quaternion case. He showed that any generalized almost quaternionic manifold equipped with an appropriate connection admit a twistor space which comes naturally equipped with a tautological almost generalized complex structure. But he has left open the problem of the integrability. The aim of this article is to give an integrability criterion for this generalized almost complex structure and to give some examples especially in the case of generalized hyperkähler manifolds using the generalized Bismut connection, introduced by Gualtieri (Branes on Poisson varieties, The many facets of geometry: a tribute to Nigel Hitchin (2010) (Oxford: Oxford University Press) pp. 368–395).

    • Author Affiliations



      1. UMR 6205, Laboratoire de Mathématique de Bretagne Atlantique, Université de Bretagne Occidentale, 29238 Brest cedex 3, France
    • Dates

  • Proceedings – Mathematical Sciences | News

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