Quaternionic Kähler Manifolds of Cohomogeneity One

四元数Kähler流形上的solvsoliton纤维化

Quaternionic Kähler manifolds fibered by solvsolitons

本文研究余维数为一的四元数Kähler流形主轨道，证明零变形参数下由solvsoliton纤维化，变形后仍为可解流形但失去Ricci孤子性质。

Quaternionic geometry in dimension eight

We describe the 8-dimensional Wolf spaces as cohomogeneity one SU(3)-manifolds, and discover perturbations of the quaternion-kaehler metric on the simply-connected 8-manifold G_2/SO(4) that carry a closed fundamental 4-form but are not Einstein.

Delaunay-type hypersurfaces in cohomogeneity one manifolds

Classical Delaunay surfaces are highly symmetric constant mean curvature (CMC) submanifolds of space forms. We prove the existence of Delaunay-type hypersurfaces in a large class of compact manifolds, using the geometry of cohomogeneity one group actions and variational bifurcation techniques. Our construction specializes to the classical examples in round spheres, and allows to obtain Delaunay-type hypersurfaces in many other ambient spaces, ranging from complex and quaternionic projective spaces to Kervaire exotic spheres.

一类局部非齐次的完备四元数Kähler流形

A class of locally inhomogeneous complete quaternionic Kähler manifolds

该数学研究证明c-map空间类中四元数Kähler流形的单圈形变局部非齐次，推出齐次c-map空间单圈形变的等距群上同调度恰为一。

Curvature of quaternionic Kähler manifolds with $S^1$-symmetry

We study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.

Complete quaternionic Kähler manifolds with finite volume ends

We construct examples of complete quaternionic Kähler manifolds with an end of finite volume, which are not locally homogeneous. The manifolds are aspherical with fundamental group which is up to an infinite cyclic extension a semi-direct product of a lattice in a semi-simple group with a lattice in a Heisenberg group. Their universal covering is a cohomogeneity one deformation of a symmetric space of non-compact type.

紧四元数凯勒对称空间的非紧全复子流形示例

An example of non-compact totally complex submanifolds of compact quaternionic Kähler symmetric spaces

本文构造了紧四元数凯勒对称空间（四元数射影空间除外）的非紧极大维全复子流形示例，分析其结构与群作用性质，并证明了相关紧子流形的存在性限制。

单圈形变q-map空间的对称性

Symmetries of one-loop deformed q-map spaces

本文研究单圈形变q-map空间的等距同构群，证明4n维形变q-map空间的等距群包含R^{n-1}仿射群与2n+1维Heisenberg群的半直积，其结构由编码q-map空间的三次仿射超曲面决定，丰富了四元数凯勒流形的对称性研究。

一类四元数 Kähler 流形上的 Hermite 结构

Hermitian structures on a class of quaternionic Kähler manifolds

本文利用 HK/QK 对应研究了一类四元数 Kähler 流形上近 Hermite 结构的可积性与共形 Kähler 条件，给出了四维流形的完整局部分类，并在特殊情形下构造了第三个典范 Hermite 结构。