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Takumi Yamada

Bio: Takumi Yamada is an academic researcher from Shimane University. The author has contributed to research in topics: Nilmanifold & Geometry and topology. The author has an hindex of 3, co-authored 11 publications receiving 24 citations.

Papers
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Takumi Yamada1
TL;DR: In this paper, a unified constructions of lattices in splittable solvable Lie groups are considered. But they do not consider a unified construction of the lattices of a lattice in polynomial time.
Abstract: In this paper, we consider a unified constructions of lattices in splittable solvable Lie groups.

5 citations

Journal ArticleDOI
Takumi Yamada1
TL;DR: In this article, the duality of Hodge numbers of compact complex nilmanifolds is considered and a compact K¨ahlerian manifold of dimension n satisfies hp,q(M) = hq,p(M), q(m) for each p, q.
Abstract: Abstract 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 citations

Journal ArticleDOI
Takumi Yamada1
TL;DR: In this article, the authors consider several invariant complex structures on a compact real nilmanifold, and study relations between these structures and Hodge numbers, and show that they are invariant to the same Hodge number.
Abstract: Abstract 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.

4 citations

Journal ArticleDOI
Takumi Yamada1
TL;DR: In this article, the relation between invariant complex structures and Hodge numbers of compact nilmanifolds was studied from a viewpoint of Lie algberas, i.e., a simply connected real nilpotent Lie group with a Γ-rational complex structure, where Γ is a lattice in N.
Abstract: Abstract 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.

4 citations

Journal ArticleDOI
TL;DR: In this paper, a relation of non-degenerate closed $2$-forms and complex structures on compact real parallelizable nilmanifolds is considered, where the complexity of the complex structures is also considered.
Abstract: In this paper, we consider a relation of non-degenerate closed $2$-forms and complex structures on compact real parallelizable nilmanifolds.

3 citations


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TL;DR: In this article, the existence of strong Kahler with torsion (SKT) metrics and of symplectic forms taming invariant complex structures on solvmanifolds was studied.
Abstract: We study the existence of strong Kahler with torsion (SKT) metrics and of symplectic forms taming invariant complex structures $J$ on solvmanifolds $G/\Gamma$ providing some negative results for some classes of solvmanifolds. In particular, we show that if either $J$ is invariant under the action of a nilpotent complement of the nilradical of $G$ or $J$ is abelian or $G$ is almost abelian (not of type (I)), then the solvmanifold $G/\Gamma$ cannot admit any symplectic form taming the complex structure $J$, unless $G/\Gamma$ is Kahler. As a consequence, we show that the family of non-Kahler complex manifolds constructed by Oeljeklaus and Toma cannot admit any symplectic form taming the complex structure.

9 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigated Lie algebras endowed with a complex symplectic structure and developed a method to construct complex-symmetric Lie algesas with dimension 4 n + 4 from those of dimension 4n.

7 citations

Journal ArticleDOI
Takumi Yamada1
TL;DR: In this article, the authors consider several invariant complex structures on a compact real nilmanifold, and study relations between these structures and Hodge numbers, and show that they are invariant to the same Hodge number.
Abstract: Abstract 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.

4 citations

Journal ArticleDOI
Takumi Yamada1
TL;DR: In this article, the relation between invariant complex structures and Hodge numbers of compact nilmanifolds was studied from a viewpoint of Lie algberas, i.e., a simply connected real nilpotent Lie group with a Γ-rational complex structure, where Γ is a lattice in N.
Abstract: Abstract 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.

4 citations

Posted Content
TL;DR: In this article, the existence of symplectic forms taming invariant complex structures on solvmanifolds G/ was studied, and it was shown that the family of non-Kahler complex manifolds constructed by Oeljeklaus and Toma cannot admit any symplectic form taming the complex structure.
Abstract: We study the existence of symplectic forms taming invariant complex structures J on solvmanifolds G/ providing some negative results. In particular, we show th at if either J is invariant under the action of a nilpotent complement of the nilradical of G or J is abelian or G is amost abelian (not of type (I)), then the solvmanifold G/ cannot admit any symplectic form taming the complex structure J, unless G/ is Kahler. As a consequence, we show that the family of non-Kahler complex manifolds constructed by Oeljeklaus and Toma cannot admit any symplectic form taming the complex structure.

3 citations