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Properties of a hypothetical exotic complex structure on P 3

J. R. Brown (2007)

Mathematica Bohemica

We consider almost-complex structures on P 3 whose total Chern classes differ from that of the standard (integrable) almost-complex structure. E. Thomas established the existence of many such structures. We show that if there exists an “exotic” integrable almost-complex structures, then the resulting complex manifold would have specific Hodge numbers which do not vanish. We also give a necessary condition for the nondegeneration of the Frölicher spectral sequence at the second level.

Propriétés globales de l'espace de twisteurs

Paolo De Bartolomeis, Luca Migliorini, Antonella Nannicini (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study global properties of the twistor space over an even dimensional conformally flat manifold, proving that the twistor space is Kähler if and only if the manifold is conformally equivalent to the standard 2 n -dimensional sphere ( n > 2 ).

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