The Map Between Conformal Hypercomplex/Hyper-Kähler and Quaternionic(-Kähler) Geometry

Communications in Mathematical Physics, Sep 2007

Eric Bergshoeff, Stefan Vandoren, Antoine Van Proeyen

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The Map Between Conformal Hypercomplex/Hyper-Kähler and Quaternionic(-Kähler) Geometry

Commun. Math. Phys. The Map Between Conformal Hypercomplex/ Hyper-Kähler and Quaternionic(-Kähler) Geometry Eric Bergshoeff 2 Stefan Vandoren 1 Antoine Van Proeyen 0 0 Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven , Celestijnenlaan 200D, B-3001 Leuven , Belgium 1 Institute for Theoretical Physics, Utrecht University , Leuvenlaan 4, 3508 TD Utrecht , The Netherlands 2 Center for Theoretical Physics, University of Groningen , Nijenborgh 4, 9747 AG Groningen , The Netherlands The sentence before (3.5) “The integrability conditions for (1.1) and (3.2) then read” should be replaced by “We demand, here and everywhere below, that the vectors k and k are 'symmetry generators' in the sense of (5.1), i.e., which is mathematically the statement that they define affine transformations. This leads to” - k X RX Y Z W = 0. (3.5) When the connection is metric, then these equations are integrability conditions for (1.1) and (3.2) using the symmetries of the Riemann tensor. Communicated by M. Aizenman (...truncated)


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Eric Bergshoeff, Stefan Vandoren, Antoine Van Proeyen. The Map Between Conformal Hypercomplex/Hyper-Kähler and Quaternionic(-Kähler) Geometry, Communications in Mathematical Physics, 2007, pp. 553, Volume 274, Issue 2, DOI: 10.1007/s00220-007-0266-7