Geodesic
Generalized Gray--Hervella classes and holomorphically projective transformations of generalized almost-Hermitian structures
Izvestiya. Mathematics , Tome 69 (2005) no. 5, pp. 963-987.

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We obtain a new description and a natural generalization of Gray–Hervella classes in the case of generalized almost-Hermitian structures. We study the singularities of holomorphically projective transformations of structures of these classes. In particular, we construct certain invariants of these transformations. We study the behaviour of Gray–Hervella classes under such transformations and, in particular, we find the classes invariant under them. 
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V. F. Kirichenko. Generalized Gray--Hervella classes and holomorphically projective transformations of generalized almost-Hermitian structures. Izvestiya. Mathematics , Tome 69 (2005) no. 5, pp. 963-987. http://geodesic.mathdoc.fr/item/IM2_2005_69_5_a2/

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