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Remarks on Hodge numbers and invariant complex structures of compact nilmanifolds

100%
Yamada T.
Complex Manifolds
|
2016
|
tom 3
|
nr 1
EN
If N is a simply connected real nilpotent Lie group with a Γ-rational complex structure, where Γ is a lattice in N, then [...] for each s, t.We study relations between invariant complex structures and Hodge numbers of compact nilmanifolds from a viewpoint of Lie algberas.
2
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Hodge numbers and invariant complex structures of compact nilmanifolds

100%
Yamada T.
Complex Manifolds
|
2016
|
tom 3
|
nr 1
EN
In this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.
3
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Duality of Hodge numbers of compact complex nilmanifolds

100%
Yamada T.
Complex Manifolds
|
2015
|
tom 2
|
nr 1
EN
A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.
4
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Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds

63%
Alekseevsky D., Kamishima Y.
Open Mathematics
|
2004
|
tom 2
|
nr 5
732-753
EN
We define notion of a quaternionic and para-quaternionic CR structure on a (4n+3)-dimensional manifold M as a triple (ω1,ω2,ω3) of 1-forms such that the corresponding 2-forms satisfy some algebraic relations. We associate with such a structure an Einstein metric on M and establish relations between quaternionic CR structures, contact pseudo-metric 3-structures and pseudo-Sasakian 3-structures. Homogeneous examples of (para)-quaternionic CR manifolds are given and a reduction construction of non homogeneous (para)-quaternionic CR manifolds is described.
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