Content deleted Content added
m →The generalized tangent bundle: Typo/general fixing, replaced: Viceversa → Vice versa using AWB |
m →The generalized tangent bundle: Changed link from 'eigenbundle' to point to a brief description on the vector bundle page |
||
Line 23:
:::<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>
Like in the case of an ordinary [[almost complex structure]], a generalized almost complex structure is uniquely determined by its <math>\sqrt{-1}</math>-[[Vector bundle#Operations on vector bundles|eigenbundle]], i.e. a subbundle <math>L</math> of the complexified generalized tangent bundle <math>(\mathbf{T}\oplus\mathbf{T}^*)\otimes\mathbb{C}</math>
given by
Line 34:
(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>-
===Courant bracket===
| |||