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replacing redirect Holomorphic to dab page with appropriate destination Holomorphic function |
m →The generalized tangent bundle: Typo/general fixing, replaced: Viceversa → Vice versa using AWB |
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Line 19:
:::<math>{\mathcal J}: \mathbf{T}\oplus\mathbf{T}^*\rightarrow \mathbf{T}\oplus\mathbf{T}^*</math>
such that
:::<math>{\mathcal J}^2=-{\rm Id},\ \ \mbox{ and }\ \ \langle {\mathcal J}(X+\xi),{\mathcal J}(Y+\eta)\rangle=\langle X+\xi,Y+\eta\rangle.</math>
Line 28:
:::<math>L=\{X+\xi\in (\mathbf{T}\oplus\mathbf{T}^*)\otimes\mathbb{C}\ :\ {\mathcal J}(X+\xi)=\sqrt{-1}(X+\xi)\}</math>
Such subbundle ''L'' satisfies the following properties:
(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]] equals ''N'' and <math>\langle\ell,\ell'\rangle=0</math> for all <math>\ell,\ell'\in L.</math>
===Courant bracket===
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