稳定广义复结构

pluriclosed 孤子与广义 Ricci 孤子的动力学稳定性

Dynamical stability of Pluriclosed and Generalized Ricci solitons

本研究探讨 pluriclosed 流与广义 Ricci 流的稳定性，证明了广义爱因斯坦 - 希尔伯特泛函二阶变分非正且无穷小形变可积时流动力学稳定，以及第一陈类消失时 pluriclosed 稳态孤子动力学稳定的结论。

Kobayashi-Hitchin correspondence of generalized holomorphic vector bundles over generalized Kahler manifolds of symplectic type

In the previous paper \cite{Goto_2017}, the notion of an Einstein-Hermitian metric of a generalized holomorphic vector bundle over a generalized Kahler manifold of symplectic type was introduced from the moment map framework. In this paper we establish a Kobayashi-Hitchin correspondence, that is, the equivalence of the existence of an Einstein-Hermitian metric and $ψ$-polystability of a generalized holomorphic vector bundle over a compact generalized Kahler manifold of symplectic type. Poisson modules provide intriguing generalized holomorphic vector bundles and we obtain $ψ$-stable Poisson mo…

Generalized Henneberg stable minimal surfaces

We generalize the classical Henneberg minimal surface by giving an infinite family of complete, finitely branched, non-orientable, stable minimal surfaces in $\mathbb{R}^3$. These surfaces can be grouped into subfamilies depending on a positive integer (called the complexity), which essentially measures the number of branch points. The classical Henneberg surface $H_1$ is characterized as the unique example in the subfamily of the simplest complexity $m=1$, while for $m\geq 2$ multiparameter families are given. The isometry group of the most symmetric example $H_m$ with a given complexity $m\i…

关于广义复结构的形变：广义Calabi-Yau情形

On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case

我们证明了扭曲广义Calabi-Yau流形上的Tian-Todorov定理的一个类似定理，即证明了紧致扭曲广义Calabi-Yau流形上的广义复结构的模空间是通畅光滑的.我们还构造了扩展的模空间并研究了它的Frobenius结构。物理意义也进行了讨论。

四维广义复结构的构造

Constructions of generalized complex structures in dimension four

利用四维流形理论研究了（扭曲）广义复结构的存在性。结果表明，存在具有多个型变轨迹的（扭曲）广义复结构。在一个例子驱动的方式，（扭曲）广义复结构被构造在无数的四个流形，无论是单连通和非单连通，既不是复杂的，也不是辛。

Generalized Kähler-Einstein metric along $\mathbb Q$-Fano fibration

In this paper, we show that along $\mathbb Q$-Fano fibration, when general fibres, base and central fiber (with at worst Kawamata log terminal singularities)are K-poly stable then there exists a relative Kähler-Einstein metric. We introduce the fiberwise Kähler-Einstein foliation and we mention that the main difficulty to obtain higher estimates is to solve relative CMA equation along such foliation. We propose a program such that for finding a pair of canonical metric $(ω_X,ω_B)$, which satisfies in $$Ric(ω_X)=π^*ω_B+π^*(ω_{WP})+[\mathcal N]$$ on K-poly stable degeneration $π:X\to B$, where $…

广义复结构与李括号

Generalized complex structures and Lie brackets

我们期待在广义复结构从泊松和狄拉克几何的角度来看，我们注意到，令人困惑的方程的概念下的广义复结构有奇迹般地简单的意义时，通过李代数/群胚。

从广义Bochner技巧的观点论极小子流形与调和映射理论

On the theory of minimal submanifolds and harmonic maps from the point of view of the generalized Bochner technique

本文从广义Bochner技巧出发，研究完备黎曼流形上的调和映射及极小与稳定极小子流形，并重新审视相关经典定理。

A note on submanifolds and mappings in generalized complex geometry

In generalized complex geometry, we revisit linear subspaces and submanifolds that have an induced generalized complex structure. We give an expression of the induced structure that allows us to deduce a smoothness criteria, we dualize the results to submersions and we make a few comments on generalized complex mappings. Then, we discuss submanifolds of generalized Kaehler manifolds that have an induced generalized Kaehler structure. These turn out to be the common invariant submanifolds of the two classical complex structures of the generalized Kaehler manifold.