A PDF file should load here. If you do not see its contents
the file may be temporarily unavailable at the journal website
or you do not have a PDF plug-in installed and enabled in your browser.
Alternatively, you can download the file locally and open with any standalone PDF reader:
http://link.springer.com/content/pdf/10.1007%2Fs00220-007-0266-7.pdf
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)