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Twistor theory for co-CR quaternionic manifolds and related structures

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Abstract

In a general and non-metrical framework, we introduce the class of co-CR quaternionic manifolds, which contains the class of quaternionic manifolds, whilst in dimension three it particularizes to give the Einstein-Weyl spaces. We show that these manifolds have a rich natural Twistor Theory and, along the way, we obtain a heaven space construction for quaternionic-Kähler manifolds.

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Authors and Affiliations

  1. Dipartimento di Matematica, Istituto “Guido Castelnuovo”, Università degli Studi di Roma “La Sapienza”, Piazzale Aldo Moro, 2, I 00185, Roma, Italia

    Stefano Marchiafava

  2. Institutul de Matematică “Simion Stoilow” al Academiei Române, C.P. 1-764, 014700, Bucureşti, România

    Radu Pantilie

Authors
  1. Stefano Marchiafava
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  2. Radu Pantilie
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Corresponding author

Correspondence to Stefano Marchiafava.

Additional information

S.M. acknowledges that this work was done under the program of GNSAGAINDAM of C.N.R. and PRIN07 “Geometria Riemanniana e strutture differenziabili” of MIUR (Italy).

R.P. acknowledges that this work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PNII-ID-PCE-2011-3-0362, and by the Visiting Professors Programme of GNSAGAINDAM of C.N.R. (Italy).

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Marchiafava, S., Pantilie, R. Twistor theory for co-CR quaternionic manifolds and related structures. Isr. J. Math. 195, 347–371 (2013). https://doi.org/10.1007/s11856-013-0001-3

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  • DOI: https://doi.org/10.1007/s11856-013-0001-3

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