Related papers: A rigidity theorem for quaternionic Kaehler struct…

In this paper, by modifying the arguments in \cite{WY}, we get some rigidity theorems on compact manifolds with nonempty boundary. The results in this paper are similar with those in \cite{ST} and \cite{WY}. Like \cite{ST} and \cite{WY}, we…

We establish a regularity result for the metric on any 4-dimensional extremal K\"ahler manifold, and a weak compactness theorem on the space of such metrics. Specifically, the sectional curvature at a point is bounded when the quantity…

In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…

We describe the topology of the moduli spaces of flat metrics for all the 3-dimensional closed manifolds. We give an algebraic description of the moduli spaces for the 4-dimensional closed flat manifolds with a single generator in their…

An Einstein manifold is called scalar curvature rigid if there are no compactly supported volume-preserving deformation of the metric which increase the scalar curvature. We give various characterizations of scalar curvature rigidity for…

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…

We explicitly describe, in the language of four-dimensional N=1 supersymmetric field theory, what happens when the moduli of a heterotic Calabi-Yau compactification change so as to make the internal non-Abelian gauge fields…

Building on the theory of noncommutative complex structures, the notion of a noncommutative K\"ahler structure is introduced. In the quantum homogeneous space case many of the fundamental results of classical K\"ahler geometry are shown to…

We present a geometric construction of a new class of hyper-Kahler manifolds with torsion. This involves the superposition of the four-dimensional hyper-Kahler geometry with torsion associated with the NS-5-brane along quaternionic planes…

We prove that a sequence of Fueter sections of a bundle of compact hyperkahler manifolds $\mathfrak X$ over a $3$-manifold $M$ with bounded energy converges (after passing to a subsequence) outside a $1$-dimensional closed rectifiable…

Let M be a compact manifold with boundary. In this paper, we discuss some rigidity theorems of metrics in a same conformal class that fixes the boundary and satisfy certain integral conditions on the the scalar curvatures and the mean…

In this paper, we establish a Liouville type rigidity result for a class of asymptotically hyperbolic non-compact Einstein metrics defined on manifolds of dimension $d\ge 5$ extending the earlier result in dimension $d=4$.

We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic…

We define a one-dimensional family of "Euler" stability conditions on $\mathbb{P}^n$ which are conjectured to converge to Gieseker stability for coherent sheaves. Here, we focus on ${\mathbb P}^3$, first identifying Euler stability…

A $p$-K\"ahler structure on a complex manifold of complex dimension $n$ is given by a $d$-closed transverse real $(p,p)$-form. In the paper we study the existence of $p$-K\"ahler structures on compact quotients of simply connected Lie…

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…

A general theorem on the existence of natural torsion-free affine connections on a complete family of compact complex submanifolds in a complex manifold is proved. Applications to twistor theory are discussed.

We define Hitchin's moduli space for a principal bundle $P$, whose structure group is a compact semisimple Lie group $K$, over a compact non-orientable Riemannian manifold $M$. We use the Donaldson-Corlette correspondence, which identifies…

In this paper we introduce the notion of rigidity for harmonic-Ricci solitons and we provide some characterizations of rigidity, generalizing some known results for Ricci solitons. In the compact case we are able to deal with not…

A non-linear generalization of the Dirac operator in 4-dimensions, obtained by replacing the spinor representation with a hyperKahler manifold admitting certain symmetries, is considered. We show that the existence of a covariantly…