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Twistor forms are a natural generalization of conformal vector fields on riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact Kähler manifolds and give a complete description up to special forms in the middle dimension. In particular, we show that they are closely related to hamiltonian 2-forms. This provides the first examples of compact Kähler manifolds with non-parallel twistor forms in any even degree.
@article{ASNSP_2003_5_2_4_823_0,
author = {Moroianu, Andrei and Semmelmann, Uwe},
title = {Twistor forms on {K\"ahler} manifolds},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {823--845},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 2},
number = {4},
year = {2003},
mrnumber = {2040645},
zbl = {1121.53050},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_823_0/}
}
TY - JOUR AU - Moroianu, Andrei AU - Semmelmann, Uwe TI - Twistor forms on Kähler manifolds JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 823 EP - 845 VL - 2 IS - 4 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_823_0/ LA - en ID - ASNSP_2003_5_2_4_823_0 ER -
%0 Journal Article %A Moroianu, Andrei %A Semmelmann, Uwe %T Twistor forms on Kähler manifolds %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 823-845 %V 2 %N 4 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_823_0/ %G en %F ASNSP_2003_5_2_4_823_0
Moroianu, Andrei; Semmelmann, Uwe. Twistor forms on Kähler manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 4, pp. 823-845. http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_823_0/