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Astheno-Kähler structures on Calabi-Eckmann manifolds

100%
Matsuo K.
Colloquium Mathematicum
|
2009
|
tom 115
|
nr 1
33-39
EN
We show that there exist astheno-Kähler structures on Calabi-Eckmann manifolds.
2
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Pseudo-Bochner-flat locally conformal Kähler submanifolds

100%
Matsuo K.
Colloquium Mathematicum
|
2007
|
tom 108
|
nr 2
305-315
EN
Let M̃ be an (m+r)-dimensional locally conformal Kähler (l.c.K.) manifold and let M be an m-dimensional l.c.K. submanifold of M̃ (i.e., a complex submanifold with the induced l.c.K. structure). Assume that both M̃ and M are pseudo-Bochner-flat. We prove that if r < m, then M is totally geodesic (in the Hermitian sense) in M̃. This is the l.c.K. version of Iwatani's result for Bochner-flat Kähler submanifolds.
3
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Pseudo-Bochner curvature tensor on Hermitian manifolds

100%
Matsuo K.
Colloquium Mathematicum
|
1999
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tom 80
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nr 2
201-209
EN
Our main purpose of this paper is to introduce a natural generalization $B_H$ of the Bochner curvature tensor on a Hermitian manifold $M$ provided with the Hermitian connection. We will call $B_H$ the pseudo-Bochner curvature tensor. Firstly, we introduce a unique tensor P, called the (Hermitian) pseudo-curvature tensor, which has the same symmetries as the Riemannian curvature tensor on a Kähler manifold. By using P, we derive a necessary and sufficient condition for a Hermitian manifold to be of pointwise constant Hermitian holomorphic sectional curvature. Our pseudo-Bochner curvature tensor $B_H$ is naturally obtained from the conformal relation for the pseudo-curvature tensor P and it is conformally invariant. Moreover we show that $B_H$ is different from the Bochner conformal tensor in the sense of Tricerri and Vanhecke.
4
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On compact astheno-Kähler manifolds

63%
Matsuo K., Takahashi T.
Colloquium Mathematicum
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2001
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tom 89
|
nr 2
213-221
EN
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.
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