| Autor: |
Deschamps, Guillaume, Du, Noël Le, Mourougane, Christophe |
| Rok vydání: |
2012 |
| Předmět: |
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| Zdroj: |
Bulletin de la soci\'et\'e math\'ematique de France, 2017, 145 (1), pp.1-27 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.24033/bsmf.2729 |
| Popis: |
We compute the hessian of the natural Hermitian form successively on the Calabi family of a hyperk\"ahler manifold, on the twistor space of a 4-dimensional anti-self-dual Riemannian manifold and on the twistor space of a quaternionic K\"ahler manifold. We show a strong convexity property of the cycle space of twistor lines on the Calabi family of a hyperk\"ahler manifold. We also prove convexity properties of the 1-cycle space of the twistor space of a 4-dimensional anti-self-dual Einstein manifold of non-positive scalar curvature and of the 1-cycle space of the twistor space of a quaternionic K\"ahler manifold of non-positive scalar curvature. We check that no non-K\"ahler strong KT manifold occurs as such a twistor space. |
| Databáze: |
arXiv |
| Externí odkaz: |
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