Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
Gualtieri,Generalized complex geometry, Ph.D
2 Pith papers cite this work. Polarity classification is still indexing.
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The Gray-Hervella classes are determined for the natural almost Hermitian structures on the product twistor space of 4-dimensional Riemannian manifolds.
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Generalised Complex and Spinor Relations
Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
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Gray-Hervella classes on product twistor spaces
The Gray-Hervella classes are determined for the natural almost Hermitian structures on the product twistor space of 4-dimensional Riemannian manifolds.