Related papers: Generalized para-K\"ahler manifolds

We introduce the concept of generalized almost plastic structure, and, on a pseudo-Riemannian manifold endowed with two $(1,1)$-tensor fields satisfying some compatibility conditions, we construct a family of generalized almost plastic…

We continue the study of blow-ups in generalized complex geometry with the blow-up theory for generalized K\"ahler manifolds. The natural candidates for submanifolds to be blown-up are those which are generalized Poisson for one of the two…

In this article, we consider the almost Hermitian structure on $TM$ induced by a pair of a metric and an affine connection on $M$. We find the conditions under which $TM$ admits almost K\"ahler structures, K\"ahler structures and Einstein…

Any quaternionic K\"ahler manifold $(\bar N,g_{\bar N},\mathcal Q)$ equipped with a Killing vector field $X$ with nowhere vanishing quaternionic moment map carries an integrable almost complex structure $J_1$ that is a section of the…

A Hermitian metric on a complex manifold of complex dimension $n$ is called {\em astheno-K\"ahler} if its fundamental $2$-form $F$ satisfies the condition $\partial \overline \partial F^{n - 2} =0$. If $n =3$, then the metric is {\em strong…

Almost hypercomplex pseudo-Hermitian manifolds are considered. Isotropic hyper-K\"ahler manifolds are introduced. A 4-parametric family of 4-dimensional manifolds of this type is constructed on a Lie group. This family is characterized…

We present a uniform framework generalising and extending the classical theories of projective differential geometry, c-projective geometry, and almost quaternionic geometry. Such geometries, which we call \emph{projective parabolic…

An {\em almost p-K\"ahler manifold} is a triple $(M,J,\Omega)$, where $(M,J)$ is an almost complex manifold of real dimension $2n$ and $\Omega$ is a closed real tranverse $(p,p)$-form on $(M,J)$, where $1\leq p\leq n$. When $J$ is…

A description of the fundamental degrees of freedom underlying generalized K\"ahler geometry, which separates its holomorphic moduli from its compatible Riemannian metric in a similar way to the K\"ahler case, has been sought since its…

Gray & Hervella gave a classification of almost Hermitian structures (g,I) into 16 classes. We systematically study the interaction between these classes when one has an almost hyper-Hermitian structure (g,I,J,K). In general dimension we…

Let $M$ be a closed symplectic manifold of dimension $2n$ with non-ellipticity. We can define an almost K\"ahler structure on $M$ by using the given symplectic form. Hence, we have a $\G=\pi_1(M)$-invariant almost K\"ahler structure on the…

We characterize general pseudo-harmonic morphisms from a Riemannian manifold to a Hermitian manifold as pseudo horizontally weakly conformal maps with an additional property. We study to what extent we can (locally) describe these…

There is a known hyperk\"ahler structure on any complexified Hermitian symmetric space $G/K$, whose construction relies on identifying $G/K$ with both a (co)adjoint orbit and the cotangent bundle to the compact Hermitian symmetric space…

We study invariant pseudo-K\"ahler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the…

A subgroup $H\leq G$ is said to be almost normal if every conjugate of $H$ is commensurable to $H$. If $H$ is almost normal, there is a well-defined quotient space $G/H$. We show that if a group $G$ has type $F_{n+1}$ and contains an almost…

In this paper, we introduce the notions of pseudo-Riemannian, para-Hermitian and para- Kahler structures on hom-Lie algebras. In addition, we present the characterization of these structures. Also, we provide an example including these…

Nearly K\"{a}hler and K\"{a}hler-Codazzi type manifolds are defined in a very similar way. We prove that nearly K\"{a}hler type manifolds have sense just in Hermitian and para-Hermitian contexts, and that K\"{a}hler-Codazzi type manifolds…

In the paper, we first study more general models, where $F$ has constant rank and is based on weak metric structures (introduced by the first author and R. Wolak), which generalize almost complex and almost contact metric $f$-contact…

In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-K\"ahler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian…

The notion of generalized almost paracontact structure on the generalized tangent bundle $TM\oplus T^*M$ is introduced and its properties are investigated. The case when the manifold $M$ carries an almost paracontact metric structure is…