Generalized complex structure: Difference between revisions

Revision as of 06:55, 16 November 2020

Revision as of 23:42, 28 March 2022

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Some of the almost structures in generalized complex geometry may be rephrased in the language of [[G-structure]]s. The word "almost" is removed if the structure is integrable.

The bundle <math>(\mathbf{T} \oplus \mathbf{T}^*) \otimes \Complex</math> with the above inner product is an {{math|O(2''n'',&nbsp; 2''n'')}} structure. A generalized almost complex structure is a reduction of this structure to a {{math|U(''n'',&nbsp; ''n'')}} structure. Therefore, the space of generalized complex structures is the coset

:<math>\frac{O(2n,2n)}{U(n,n)}.</math>