相关论文: On differential geometry of non-degenerate CR mani…

We give several versions of Siu's $\partial\bar{\partial}$-formula for maps from a strictly pseudoconvex pseudo-Hermitian manifold $(M^{2m+1}, \theta)$ into a K\"ahler manifold $(N^n, g)$. We also define and study the notion of…

Motivated by the geometry of Levi degenerate CR hypersurfaces, we define a pre-K\"ahler structure on a complex manifold as a pre-symplectic structure compatible with the almost complex structure, i.e. a closed (1,1)-form. Extending Freeman…

Let M be a hypercomplex Hermitian manifold, (M,I) the same manifold considered as a complex Hermitian with a complex structure I induced by the quaternions. The standard linear-algebraic construction produces a canonical nowhere degenerate…

This is the very first paper to focus on the CR analogue of Yau's uniformization conjecture in a complete noncompact pseudohermitian $(2n+1)$-manifold of vanishing torsion (i.e. Sasakian manifold) which is an odd dimensional counterpart of…

Let $(\acute{N},g,\nabla )$\ be a $2n$-dimensional quasi-statistical manifold that admits a pseudo-Riemannian metric $g$ (or $h)$ and a linear connection $\nabla $ with torsion. This paper aims to study an almost Hermitian structure $(g,L)$…

We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields $h:=\frac{1}{2}\pounds _\xi \varphi$ and $\ell := R(\cdot,\xi)\xi$, emphasizing analogies and differences with respect to the contact metric case.…

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 investigate degenerate special-Hermitian metrics on compact complex manifolds, in particular, degenerate K\"ahler and locally conformally K\"ahler metrics on special classes of non-K\"ahler manifolds.

On a para-quaternionic K\"ahler manifold $(\widetilde M^{4n},Q,\widetilde g)$, which is first of all a pseudo-Riemannian manifold, a natural definition of (almost) K\"ahler and (almost) para-K\"ahler submanifold $(M^{2m},\mathcal{J},g)$ can…

Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong…

In this article, we examine the behavior of the Riemannian and Hermitian curvature tensors of a Hermitian metric, when one of the curvature tensors obeys all the symmetry conditions of the curvature tensor of a K\"ahler metric. We will call…

In this paper, we study a special type of compact Hermitian manifolds that are Strominger K\"ahler-like, or SKL for short. This condition means that the Strominger connection (also known as Bismut connection) is K\"ahler-like, in the sense…

We study two kinds of curvature invariants of Riemannian manifold equip\-ped with a complex distribution $D$ (for example, a CR-submanifold of an almost Hermitian manifold) related to sets of pairwise orthogonal subspaces of the…

A contact manifold $M$ can be defined as a quotient of a symplectic manifold $X$ by a proper, free action of $\R^{>0}$, with the symplectic form homogeneous of degree 2. If $X$ is, in addition, Kaehler, and its metric is also homogeneous of…

In the first part, Hyperkaehler Embeddings and Holomorphic symplectic Geometry I, we prove the following. Let $N$ be a closed analytic subvariety of a generic deformation of a holomorphically symplectic compact manifold $M$. Then the…

In this paper we introduce paraquaternionic CR-submanifolds of almost paraquaternionic hermitian manifolds and state some basic results on their differential geometry. We also study a class of semi-Riemannian submersions from…

We study non-degenerate CR geometries of hypersurface type that are symmetric in the sense that, at each point, there is a CR transformation reversing the CR distribution at that point. We show that such geometries are either flat or…

In this paper, we study a general almost Schur Lemma on pseudo-Hermitian (2n+1)-manifolds $(M,J,\theta)$ for $n\geq2$. When the equality of almost Schur inequality holds, we derive the contact form $\theta$ is pseudo-Einstein and the…

Germs of locally homogeneous CR manifolds M can be characterized in terms of certain algebraic data, e.g., by CR-algebras. We give an explicit formula which relates the Levi form of such an M and its higher order analogues to the Lie…

In this paper we study the para-hyperK\"ahler geometry of the deformation space of MGHC anti-de Sitter structures on $\Sigma\times\mathbb R$, for $\Sigma$ a closed oriented surface. We show that a neutral pseudo-Riemannian metric and three…