Generalized Kählerian manifolds and transformation of generalized contact structures. (English) Zbl 1424.53115

Let \(M\) be an even-dimensional smooth manifold. A generalized complex structure on \(M\) is given by a bundle homomorphism \(J:TM\oplus T^*M\to TM\oplus T^*M\) which preserves the natural parity, \(J^2=-I\), and satisfies integrability conditions. A generalized Kähler structure on \(M\) is a pair of commuting generalized complex structures such that they define a positive definite metric on \(TM\oplus T^*M\) (see [N. Hitchin, Surv. Differ. Geom. 16, 79–124 (2011; Zbl 1252.53096)].
In the paper under review the authors apply \(D\)-homothetic bi-warping (see [B. Gherici and B. Mohamed, Afr. Diaspora J. Math. 21, No. 2, 1–14 (2018; Zbl 1409.53028); D. E. Blair, Publ. Inst. Math., Nouv. Sér. 94(108), 47–54 (2013; Zbl 1299.53001)]) in order to construct generalized Kähler structures starting from classical odd-dimensional almost contact metric structure or even-dimensional almost Kähler manifold. Also, they extend the \(D\)-homothetic bi-warping to generalized Riemannian manifolds.


53D18 Generalized geometries (à la Hitchin)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C10 \(G\)-structures
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