相关论文: Cohomological properties of Hermitian symplectic t…

Let $(M, \Omega)$ be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration $\pi: M \to B$, and $\eta$ a closed $(1,1)$-form on $B$. Then $\Omega+ \pi^* \eta$ is a holomorphically symplectic form on a complex…

We study almost Hermitian 4-manifolds with holonomy algebra, for the canonical Hermitian connection, of dimension at most one. We show how Riemannian 4-manifolds admitting five orthonormal symplectic forms fit therein and classify them. In…

Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a…

We introduce the notion of a special complex manifold: a complex manifold (M,J) with a flat torsionfree connection \nabla such that (\nabla J) is symmetric. A special symplectic manifold is then defined as a special complex manifold…

Let $(M,J)$ be a $n$-dimensional complex manifold: a $p$-K\"ahler structure (resp. $p$-symplectic structure) on $M$ is a real, closed $(p,p)$-transverse form $\Omega$ (resp. real, closed $2p$-form whose $(p,p)$-component is transverse). We…

In the present paper we study the variation of the dimensions $h_k$ of spaces of symplectically harmonic cohomology classes (in the sense of Brylinski) on closed symplectic manifolds. We give a description of such variation for all…

Let $M$ be an irreducible Hermitian symmetric space of compact type, and let $\omega$ be its K\"ahler form. For a triplet $(p_1,p_2,p_3)$ of points in $M$ we study conditions under which a geodesic triangle $\mathcal T(p_1,p_2,p_3)$ with…

Answering a conjecture by S. Kobayashi, in 1986, K. Sekigawa and L. Vanhecke proved that an almost hermitian manifold whose local geodesic symmetries preserve the K\"ahler 2-form is a locally symmetric hermitian space. In the present paper,…

On a complex manifold $(M,J)$, we interpret complex symplectic and pseudo-K\"ahler structures as symplectic forms with respect to which $J$ is, respectively, symmetric and skew-symmetric. We classify complex symplectic structures on…

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…

A Hermitian metric on a complex manifold is called strong K\"ahler with torsion (SKT) if its fundamental 2-form $\omega$ is $\partial \bar \partial$-closed. We review some properties of strong KT metrics also in relation with symplectic…

With the aid of the theory of Jordan triple systems, we construct an explicit bi-symplectomorphism between a Hermitian symmetric space of non-compact type and $\C^n$ equipped with both the flat Kaehler-form and the Fubini-Study form. Our…

A symplectic toric orbifold is a compact connected orbifold $M$, a symplectic form $\omega$ on $M$, and an effective Hamiltonian action of a torus $T$ on $M$, where the dimension of $T$ is half the dimension of $M$. We prove that there is a…

Let (M,\omega) be a symplectic manifold, and Sigma a compact Riemann surface. We define a 2-form on the space of immersed symplectic surfaces in M, and show that the form is closed and non-degenerate, up to reparametrizations. Then we give…

We provide a closed, simply connected, symplectic $6$-manifold having infinitely many codimension $2$ symplectic submanifolds. These are mutually homologous but homotopy inequivalent, and furthermore, they cannot admit complex structures.…

In this note we prove that a positive multiple of each even-dimensional integral homology class of a compact symplectic manifold $(M^{2n}, \omega)$ can be represented as the difference of the fundamental classes of two symplectic…

A Hermitian-symplectic metric is a Hermitian metric whose K\"ahler form is given by the $(1,1)$-part of a closed $2$-form. Streets-Tian Conjecture states that a compact complex manifold admitting a Hermitian-symplectic metric must be…

A Hermitian-symplectic metric is a Hermitian metric whose K\"ahler form is given by the $(1,1)$-part of a closed $2$-form. Streets-Tian Conjecture states that a compact complex manifold admitting a Hermitian-symplectic metric must be…

We study the integrability of a (almost) complex structure calibrated by a symplectic form. We find new sufficent conditions.

For a symplectic manifold $(M,\omega)$, not necessarily hard Lefschetz, we prove a version of the Merkulov $d\delta$--lemma. We also study the $d\delta$--lemma and related cohomologies for compact symplectic solvmanifolds.