Abstract
We present a study of natural almost Hermitian structures on twistor spaces of quaternionic Kahler manifolds. This is used to supply (4n + 2)-dimensional examples (n > 1) of symplec tic non-Kähler manifolds. Studying their curvature properties we give a negative answer to the questions raised by D.Blair-S.Ianus and A.Gray, respectively, of whether a compact almost Kähler manifold with Hermitian Ricci tensor or whose curvature tensor belongs to the class AH2 is Kähler.
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Dedicated to Professor Helmut Karzel on the occasion of his 70th birthday
Research partially supported by Contracts MM 413/1994 and MM 423/1994 with the Ministry of Science and Education of Bulgaria and by Contract 219/1994 with the University of Sofia „St. Kl. Ohridski“.
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Alexandrov, B., Grantcharov, G. & Ivanov, S. Curvature properties of twistor spaces of quaternionic Kähler manifolds. J Geom 62, 1–12 (1998). https://doi.org/10.1007/BF01237595
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DOI: https://doi.org/10.1007/BF01237595