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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonexistence of $ 4$-dimensional almost Kaehler manifolds of constant curvature


Author: David E. Blair
Journal: Proc. Amer. Math. Soc. 110 (1990), 1033-1039
MSC: Primary 53C55; Secondary 53C15
MathSciNet review: 1043404
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Abstract: It is shown that in dimension 4 there are no almost Kaehler manifolds of constant curvature unless the constant is 0, in which case the manifold is Kaehlerian. This was previously shown in dimensions $ \geq 8$ by Z. Olszak and remains open in dimension 6.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1043404-2
PII: S 0002-9939(1990)1043404-2
Keywords: Almost Kaehler manifolds, constant curvature, quaternionic analysis, left regular function
Article copyright: © Copyright 1990 American Mathematical Society