Generalized complex structure: Difference between revisions

Revision as of 21:39, 29 April 2025

Revision as of 21:41, 29 April 2025

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:<math>\langle X+\xi,Y+\eta\rangle=\frac{1}{2}(\xi(Y)+\eta(X))=\frac{1}{2}(\varepsilon(Y,X)+\varepsilon(X,Y))=0</math>

and so <math>L(\mathbf{E}, \varepsilon)</math> is isotropic. Furthermore, <math>L(\mathbf{E}, \varepsilon)</math> is maximal because there are <math>\dim(\mathbf{E})</math> (complex) dimensions of choices for <math>\mathbf{E},</math> and <math>\varepsilon</math> is unrestricted on the [[complement (complexity)|complement]] of <math>\mathbf{E}^*,</math> which is of (complex) dimension <math>n-\dim(\mathbf{E}).</math> Thus the total (complex) dimension inis ''n''. Gualtieri has proven that all maximal isotropic subbundles are of the form <math>L(\mathbf{E}, \varepsilon)</math> for some <math>\mathbf{E}</math> and <math>\varepsilon.</math>

===Type===