Generalized complex structure: Difference between revisions

Revision as of 15:02, 25 June 2013

Revision as of 15:57, 25 June 2013

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(i) the intersection with its [[complex conjugate]] is the zero section: <math>L\cap\overline{L}=0</math>;

(ii) ''L'' is '''maximal isotropic''', i.e. its complex [[rank (linear algebra)|rank]]{{dn|date=June 2013}} equals ''N'' and <math>\langle\ell,\ell'\rangle=0</math> for all <math>\ell,\ell'\in L.</math>

Viceversa, any subbundle ''L'' satisfying (i), (ii) is the <math>\sqrt{-1}</math>-[[eigenbundle]] of a unique generalized complex structure, so that the properties (i), (ii) can be considered as an alternative definition of generalized almost complex structure.