Almost complex structures on cotangent bundles and generalized geometry
Let \(M\) be a smooth manifold with a torsion free connection \(\nabla\). The author studies a generalized complex structure of \(M\) as a complex structure on \(E = TM\oplus TM^{\star}\) and a class of such structures. The concept of \(\nabla\)-integrability was introduced for complex structures and here the integrability conditions are studied. In the case of the generalized complex structures introduced by \textit{N. Hitchin} [Q. J. Math. 54, No.~3, 281--308 (2003; Zbl 1076.32019)], the author compares the two concepts of integrability. The conditions under which they coincide are investigated.
scientific article; zbMATH DE number 5791214