关于余齐一六维流形上平衡度量的存在性

六维殆幂零可解流形上的埃尔米特结构

Hermitian structures on six-dimensional almost nilpotent solvmanifolds

本研究完成了六维强幺模殆幂零李代数的复结构分类，确定了对应可解流形的不变复结构及多种特殊埃尔米特度量的存在性，证实了相关猜想并证明了辛驯复结构的部分不存在性结果。

Compatibility of balanced and SKT metrics on two-step solvable Lie groups

It has been conjectured by Fino and Vezzoni that a compact complex manifold admitting both a compatible SKT and a compatible balanced metric also admits a compatible Kähler metric. Using the shear construction and classification results for two-step solvable SKT Lie algebras from our previous work, we prove this conjecture for compact two-step solvmanifolds endowed with an invariant complex structure which is either (a) of pure type or (b) of dimension six. In contrast, we provide two counterexamples for a natural generalisation of this conjecture in the homogeneous invariant setting. As part …

Locally conformally balanced metrics on almost abelian Lie algebras

We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable Lie algebras admitting an abelian ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional almost abelian Lie algebras admitting locally conformally balanced metrics and study some compatibility results between different types of special Hermitian metrics on almost abelian Lie groups and their compact quotients. We end by classifying almost abelian Lie algebras admitting locally conformally hyperkähler structures.

六维流形上的Hermite结构

Hermitian structures on six dimensional nilmanifolds

设（J，g）是紧致流形M上的Hermite结构，具有不变的复结构J和相容度量g，g不要求是不变的.给出了具有挠、平衡或局部共形Kähler结构（J，g）的强Kähler的6维幂零流形M的分类.

Balanced Hermitian structures on almost abelian Lie algebras

We study balanced Hermitian structures on almost abelian Lie algebras, i.e. on Lie algebras with a codimension-one abelian ideal. In particular, we classify six-dimensional almost abelian Lie algebras which carry a balanced structure. It has been conjectured by A. Fino and L. Vezzoni that a compact complex manifold admitting both a balanced metric and a SKT metric necessarily has a Kähler metric: we prove this conjecture for compact almost abelian solvmanifolds with left-invariant complex structures. Moreover, we investigate the behaviour of the flow of balanced metrics introduced by L. Bedull…

6-球面和一对3-球面的乘积上的新的G2完整锥和奇异的近Kaehler结构

New G2 holonomy cones and exotic nearly Kaehler structures on the 6-sphere and the product of a pair of 3-spheres

有一个丰富的理论，所谓的（严格）几乎Kaehler流形，几乎厄米特流形推广著名的殆复结构上的6-球诱导的八元数乘法。几乎Kaehler 6-流形在一般结构理论中扮演着重要的角色，也因为它们与奇异空间和紧例外李群的和乐群G2的联系：黎曼6-流形M上的度量锥具有包含在G2中的和乐群当且仅当M是几乎Kaehler 6-流形。该领域的一个中心问题是缺乏任何完全不均匀的例子。通过证明在6-球面和一对3-球面的乘积上至少存在一个上齐次的近似Kaehler结构，证明了第一完全非齐次近似Kaehler 6-流形的存在性.我们猜想，这些是唯一的单连通（非齐次）cohomogeneity一个几乎Kaehler结构在六个维度。

扭曲笛卡尔积上的平衡埃尔米特结构

Balanced Hermitian structures on twisted cartesian products

研究两个埃尔米特李代数根据表示ρ1和ρ2的扭曲笛卡尔积上的埃尔米特结构，给出其平衡和局部共形平衡的条件，并分类六维平衡埃尔米特扭曲笛卡尔积李代数。

具有更大紧对称性的多环面几何

Multi-toric geometries with larger compact symmetry

本文研究具有特殊和乐的多环面流形在包含环面的非阿贝尔对称群作用下的分类，证明 Spin(7) 情形仅有 T^3×SU(2) 余齐性二作用结构，并进一步分析 G_2、Calabi-Yau 与 hyperKähler 情形，最后构造了具有秩一稳定化子奇异轨道的局部例子。

Hermitian structures on a class of almost nilpotent solvmanifolds

In this paper we investigate the existence of invariant SKT, balanced and generalized Kähler structures on compact quotients $Γ\backslash G$, where $G$ is an almost nilpotent Lie group whose nilradical has one-dimensional commutator and $Γ$ is a lattice of $G$. We first obtain a characterization of Hermitian almost nilpotent Lie algebras $\mathfrak{g}$ whose nilradical $\mathfrak{n}$ has one-dimensional commutator and a classification result in real dimension six. Then, we study the ones admitting SKT and balanced structures and we examine the behaviour of such structures under flows. In parti…

具有全纯平凡典范丛的六维齐性空间

Six dimensional homogeneous spaces with holomorphically trivial canonical bundle

本研究分类了6维幺模李代数，得到具有全纯平凡典范丛的紧齐性空间，还证明了紧非凯勒平衡齐性空间中Hull-Strominger系统不变解的唯一性，并在Nakamura流形上构造了杂弦运动方程的解。