60 citations · 175 across the 41 of their papers we have counts for
43 papers
Partially Hyperbolic Compact Complex Manifolds
Hisashi Kasuya, Dan Popovici
We propose and investigate two types, the latter with two variants, of notions of partial hyperbolicity accounting for several classes of compact complex manifolds behaving hyperbo…
Complex non-Kähler manifolds that are cohomologically close to, or far from, being Kähler
Hisashi Kasuya, Jonas Stelzig
We give four constructions of non- (hence non-Kähler) manifolds: (1) A simply connected page---manifold (2) A simply connected $dd^c+…
Uniformizations of compact Sasakian manifolds
Hisashi Kasuya, Natsuo Miyatake
We give a criterion for compact Sasakian manifolds to be deformed to Sasakian manifolds which are locally isomorphic to circle bundles of anti-canonical bundles over Hermitian symm…
Categories of complex variations of Hodge structure over compact K"ahler manifolds
Hisashi Kasuya
We give a complex polarized variation of Hodge structure over a compact K"ahler manifold which controls all finite-dimensional complex polarized variations of Hodge structure o…
Double sided torus actions and complex geometry on
Hiroaki Ishida, Hisashi Kasuya
We construct explicit complex structures and transversely Kähler holomorphic foliations on corresponding to variations of real quadratic equations on a complex quadric in $…
Cohomology of holomorphic line bundles and Hodge symmetry on Oeljeklaus-Toma manifolds
Hisashi Kasuya
We prove the Hodge symmetry type result on the Dolbeault cohomology of Oeljeklaus-Toma manifolds with values in the direct sum of holomorphic line bundles. Consequently, we show th…
Frölicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds
Hisashi Kasuya, Jonas Stelzig
For complex parallelisable manifolds , with a solvable or semisimple complex Lie group, the Frölicher spectral sequence degenerates at the second page. In the so…
Remarks on Dolbeault cohomology of Oeljeklaus-Toma manifolds and Hodge theory
Hisashi Kasuya
We give explicit harmonic representatives of Dolbeault cohomology of Oeljeklaus-Toma manifolds and show that they are geometrically Dolbeault formal. We also give explicit harmonic…
Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds
Hisashi Kasuya
For a -dimensional compact Sasakian manifold, if , we prove that the analytic germ of the variety of representations of the fundamental group at every semi-simple rep…
Non-invariant deformations of left-invariant complex structures on compact Lie groups
Hiroaki Ishida, Hisashi Kasuya
We consider deformations of left-invariant complex structures on simply connected semisimple compact Lie groups which are a priori non-invariant. Computing their cohomologies, we s…
Higgs bundles and flat connections over compact Sasakian manifolds
Indranil Biswas, Hisashi Kasuya
Given a compact Kähler manifold , there is an equivalence of categories between the completely reducible flat vector bundles on and the polystable Higgs bundles o…
Morgan's mixed Hodge structures and nonabelian Hodge structures
Hisashi Kasuya
We refine the Morgan's work on mixed Hodge structures on Sullivan's --minimal models by using non-abelian Hodge theory. As an application, we give explicit representatives of re…
Transverse Kähler structures on central foliations of complex manifolds
Hiroaki Ishida, Hisashi Kasuya
For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holo…
Techniques of constructions of variations of mixed Hodge structures
Hisashi Kasuya
We give a way of constructing real variations of mixed Hodge structures over compact Kähler manifolds by using mixed Hodge structures on Sullivan's -minimal models of certain di…
Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds
Hisashi Kasuya
We show that the Malcev Lie algebra of the fundamental group of a compact -dimensional Sasakian manifold with admits a quadratic presentation by using Morgan's bigra…
Cohomologies of Sasakian groups and Sasakian solvmanifolds
Hisashi Kasuya
We show certain symmetry of the dimensions of cohomologies of the funda- mental groups of compact Sasakian manifolds by using the Hodge theory of twisted basic cohomology. As appli…
Tamed symplectic structures on compact solvmanifolds of completely solvable type
Anna Fino, Hisashi Kasuya
A compact solvmanifold of completely solvable type, i.e. a compact quotient of a completely solvable Lie group by a lattice, has a Kähler structure if and only if it is a complex t…
Extended simplicial rational Nomizu's Theorem
Hisashi Kasuya
For a torsion-free virtually polycyclic group , we give a canonical homomorphism form certain finite-dimensional cochain complex to the $\Q$-polynomial de Rham complex of the si…
Hodge theory for twisted differentials
Daniele Angella, Hisashi Kasuya
We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class $\mathcal{C}…
Cohomologies of generalized complex manifolds and nilmanifolds
Daniele Angella, Simone Calamai, Hisashi Kasuya
We study generalized complex cohomologies of generalized complex structures constructed from certain symplectic fibre bundles over complex manifolds. We apply our results in the ca…
Twisted Lefschetz numbers of infra-solvmanifolds and algebraic groups
Hisashi Kasuya
Twisted Lefschetz numbers are extensions of the ordinary Lefschetz numbers for cohomologies with values in flat bundles. As a generalization of linearization formula for the ordina…
Lefschetz coincidence numbers of solvmanifolds with Mostow conditions
Hisashi Kasuya
For any two continuous maps between two solvmanifolds of same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence numbe…
Singularity of the varieties of representations of lattices in solvable Lie groups
Hisashi Kasuya
For a lattice of a simply connected solvable Lie group , we describe the analytic germ in the variety of representations of at the trivial representation as an analytic…
Central theorems for cohomologies of certain solvable groups
Hisashi Kasuya
We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be computed by the rational…