Generalized complex structure: Difference between revisions

Revision as of 23:42, 28 March 2022

Revision as of 23:43, 28 March 2022

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Such subbundle ''L'' satisfies the following properties:

{{ordered list | list-style-type=lower-roman

(i)|1= the intersection with its [[complex conjugate]] is the zero section: <math>L\cap\overline{L}=0</math>;

(ii)|2= ''L'' is '''maximal isotropic''', i.e. its complex [[rank (linear algebra)|rank]] equals ''N'' and <math>\langle\ell, \ell' \rangle =0</math> for all <math>\ell,\ell'\in L.</math>}}

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

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