Aspherical Kähler Manifolds with Solvable Fundamental Group

具有根子群的等距群，以及具有大对称性的非球面黎曼流形 I

Isometry groups with radical, and aspherical Riemannian manifolds with large symmetry I

本文为具有大对称性的非球面黎曼流形构造了不承载局部齐性度量的例子，通过无穷小可解塔刻画连续对称性。

Geometrical formality of solvmanifolds and solvable Lie type geometries

We show that for a Lie group $G=\R^{n}\ltimes_ϕ \R^{m}$ with a semisimple action $ϕ$ which has a cocompact discrete subgroup $Γ$, the solvmanifold $G/Γ$ admits a canonical invariant formal (i.e. all products of harmonic forms are again harmonic) metric. We show that a compact oriented aspherical manifold of dimension less than or equal to 4 with the virtually solvable fundamental group admits a formal metric if and only if it is diffeomorphic to a torus or an infra-solvmanifold which is not a nilmanifold.

关于抛物结构与闭非球面流形的自同构群

On the automorphism group of parabolic structures and closed aspherical manifolds

本文研究闭非球面抛物 ${\sfG}$-流形的自同构群，证明某些抛物结构会强烈限制流形拓扑，并刻画了具有几乎可解基本群的标准 $CR$-流形与四元数接触流形的商结构。

Global linearizable actions on topological manifolds

Let $M$ be a finite dimensional topological aspherical manifold whose universal cover is ${\bf R}^n$. In this paper, we study $Aff(M)$, the subgroup of the group of homeomorphisms of $M$, whose elements can be lifted to affine transformations of ${\bf R}^n$. We show that if $M$ is closed, the connected component $Aff(M)_0$ of $Aff(M)$ acts locally freely on $M$. We deduce that $Aff(M)_0$ is a solvable Lie group, and is nilpotent if $M$ is a polynomial manifold. We study the foliation defined by the orbits of $Aff(M)_0$ if $dim(Aff(M)_0)=dim(M)-1$.

Vaisman Solvmanifolds 作为 Kodaira-Thurston Nilmanifolds 的有限商

Vaisman Solvmanifolds as Finite Quotients of Kodaira-Thurston Nilmanifolds

本文证明了所有 Vaisman 线性流形都是 Kodaira-Thurston 流形的有限商，并探讨了相关流形的结构与性质。