Abstract
In a recent paper a class of complex, compact and non-Kählerian manifolds was constructed by S. López de Medrano and A. Verjowsky. This class contains as particular cases Calabi-Eckmann manifolds, almost all Hopf manifolds and many of the examples given previously by J.-J. Loeb and M. Nicolau. In this paper we show that these manifolds are endowed with a natural non-singular vector field which is transversely Kählerian, and that analytic subsets of appropriate dimensions are tangent to this vector field. This permits to give a precise description of these sets in the generic case. In the proof, an important role is played by some complex abelian groups which are biholomorphic to big domains in these manifolds.
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References
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J.-J. Loeb and M. Nicolau,Holomorphic flows and complex structures on products of odd dimensional spheres, Mathematische Annalen306 (1996), 781–817.
S. López de Medrano and A. Verjovsky,A new family of complex, compact, nonsymplectic manifolds, Boletim da Sociedade Brasileira de Matemtica28 (1997), 1–20.
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Partially supported by the DGICYT (grant PB93-0861).
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Loeb, J.J., Nicolau, M. On the complex geometry of a class of non-Kählerian manifolds. Isr. J. Math. 110, 371–379 (1999). https://doi.org/10.1007/BF02808191
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DOI: https://doi.org/10.1007/BF02808191