On compact non-Kählerian manfolds admitting an almost Kähler structure
Holubowicz, Ryszard, Mozgawa, Witold
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Holubowicz, Ryszard, Mozgawa, Witold
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Sakane, Y. (1999)
Lobachevskii Journal of Mathematics
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Koji Matsuo, Takao Takahashi (2001)
Colloquium Mathematicae
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We prove that every compact balanced astheno-Kähler manifold is Kähler, and that there exists an astheno-Kähler structure on the product of certain compact normal almost contact metric manifolds.
Włodzimierz Jelonek (2001)
Annales Polonici Mathematici
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We describe homogeneous manifolds with generic Ricci tensor. We also prove that if 𝔤 is a 4-dimensional unimodular Lie algebra such that dim[𝔤,𝔤] ≤ 2 then every left-invariant metric on the Lie group G with Lie algebra 𝔤 admits two mutually opposite compatible left-invariant almost Kähler structures.
Lemence, R.S., Oguro, T., Sekigawa, K. (2004)
International Journal of Mathematics and Mathematical Sciences
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Zbigniew Olszak (2003)
Colloquium Mathematicae
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It is proved that there exists a non-semisymmetric pseudosymmetric Kähler manifold of dimension 4.
Wafaa Batat, P. M. Gadea, Jaime Muñoz Masqué (2012)
Annales Polonici Mathematici
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The homogeneous quaternionic Kähler structures on the Alekseevskian 𝒲-spaces with their natural quaternionic structures, each of these spaces described as a solvable Lie group, and the type of such structures in Fino's classification, are found.
Andrei Moroianu (2015)
Complex Manifolds
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We show that for n > 2 a compact locally conformally Kähler manifold (M2n , g, J) carrying a nontrivial parallel vector field is either Vaisman, or globally conformally Kähler, determined in an explicit way by a compact Kähler manifold of dimension 2n − 2 and a real function.
Lucia Alessandrini, Marco Andreatta (1987)
Compositio Mathematica
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Koji Matsuo (2009)
Colloquium Mathematicae
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We show that there exist astheno-Kähler structures on Calabi-Eckmann manifolds.
Simone Calamai, David Petrecca (2017)
Complex Manifolds
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In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.