115 research outputs found
Inequalities \`a la Fr\"olicher and cohomological decompositions
We study Bott-Chern and Aeppli cohomologies of a vector space endowed with
two anti-commuting endomorphisms whose square is zero. In particular, we prove
an inequality \`a la Fr\"olicher relating the dimensions of the Bott-Chern and
Aeppli cohomologies to the dimensions of the Dolbeault cohomologies. We prove
that the equality in such an inequality \`a la Fr\"olicher characterizes the
validity of the so-called cohomological property of satisfying the
-Lemma. As an application, we study cohomological
properties of compact either complex, or symplectic, or, more in general,
generalized-complex manifolds.Comment: to appear in J. Noncommut. Geo
Contact Calabi-Yau manifolds and Special Legendrian submanifolds
We consider a generalization of Calabi-Yau structures in the context of
-Sasakian manifolds. We study deformations of a special class of
Legendrian submanifolds and classify invariant contact Calabi-Yau structures on
5-dimensional nilmanifolds. Finally we generalize to codimension .Comment: 16 pages, no figures. Final version to appear in "Osaka J. Math.
On the cohomology of almost complex and symplectic manifolds and proper surjective maps
Let be an almost-complex manifold. In \cite{li-zhang} Li and Zhang
introduce H^{(p,q),(q,p)}_J(X)_{\rr} as the cohomology subgroups of the
-th de Rham cohomology group formed by classes represented by real
pure-type forms. Given a proper, surjective, pseudo-holomorphic map between two
almost-complex manifolds we study the relationship among such cohomology
groups. Similar results are proven in the symplectic setting for the cohomology
groups introduced in \cite{tsengyauI} by Tseng and Yau and a new
characterization of the Hard Lefschetz condition in dimension is provided
Complex symplectic structures and the -lemma
In this paper we study complex symplectic manifolds, i.e., compact complex
manifolds which admit a holomorphic -form which is
-closed and non-degenerate, and in particular the Beauville-Bogomolov-Fujiki
quadric associated to them. We will show that if X satisfies the
-lemma, then is smooth if and only if
and is irreducible if and only if .Comment: 12 page
Moduli space of CR-projective complex foliated tori
We study the moduli space of CR-projective complex foliated tori. We describe
it in terms of isotropic subspaces of Grassmannian and we show that it is a
normal complex analytic space
Bott-Chern Harmonic Forms on Stein Manifolds
Let be an -dimensional -bounded Stein manifold , i.e., a complex
-dimensional manifold admitting a smooth strictly plurisubharmonic
exhaustion and endowed with the K\"ahler metric whose fundamental form
is , such that
has bounded norm. We prove a vanishing
result for harmonic forms with respect to the Bott-Chern Laplacian on
.Comment: 11 page
Generalized G_2-manifolds and SU(3)-structures
We construct a compact example of 7- dimensional manifold endowed with a
weakly integrable generalized G_2-structure with respect to a closed and non
trivial 3-form. Moreover, we investigate which type of SU(3)-structures on a
6-dimensional manifold N give rise to a strongly integrable generalized
G_2-structure with respect to a non trivial 3-form on the product .Comment: Removed a section and added another one. Final version will appear in
Internat. J. Mat
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