Kähler and Sasakian-Einstein Quotients

Sasakian nilmanifolds

We prove that a compact nilmanifold admits a Sasakian structure if and only if it is a compact quotient of the generalized Heisenberg group of odd dimension by a co-compact discrete subgroup.

Metric Reduction and Generalized Holomorphic Structures

In this paper, metric reduction in generalized geometry is investigated. We show how the Bismut connections on the quotient manifold are obtained from those on the original manifold. The result facilitates the analysis of generalized K$\ddot{a}$hler reduction, which motivates the concept of metric generalized principal bundles and our approach to construct a family of generalized holomorphic line bundles over $\mathbb{C}P^2$ equipped with some non-trivial generalized K$\ddot{a}$hler structures.

Sasakian流形上Reeb场的闭轨道与Vaisman流形上的椭圆曲线

Closed orbits of Reeb fields on Sasakian manifolds and elliptic curves on Vaisman manifolds

本文研究Vaisman流形上闭椭圆曲线与Sasakian流形上Reeb闭轨道的计数，证明二者数量要么无穷，要么等于相应Kähler orbifold的Betti数总和。

横向凯勒几乎接触度量李代数

Transversely Kähler almost contact metric Lie algebras

研究横向凯勒几乎接触度量李代数的结构，分类最大秩的η-爱因斯坦横向凯勒结构，探讨其与准萨克西安和反准萨克西安李代数的关系。

Sasakian quiver gauge theories and instantons on the conifold

We consider Spin(4)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form $M^d \times T^{1,1}$, where $M^d$ is a smooth manifold and $T^{1,1}$ is a five-dimensional Sasaki-Einstein manifold Spin(4)/U(1). We obtain new quiver gauge theories on $M^d$ extending those induced via reduction over the leaf spaces $\mathbb{C}P^1 \times \mathbb{C}P^1$ in $T^{1,1}$. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin(4)-equivariant instantons on the conifold which is realized as the metric cone over $T^{1,1}$. We give an explicit construction …

Sasakian 流形与 Vaisman 流形上的超对称和 Hodge 理论

Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds

本文构造 Sasakian 流形对应的李超代数，并据此无坐标证明其与 Vaisman 流形上调和形式及上同调的 Hodge 分解结果，还显式计算了超对称代数。

New Einstein Metrics in Dimension Five

The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein metrics on $\scriptstyle{S^2\times S^3}$ and on $\scriptstyle{(S^2\times S^3)# (S^2\times S^3).}$ These give the first known examples of non-regular Sasakian-Einstein 5-manifolds. Our method involves describing the Sasakian-Einstein structures as links of certain isolated hypersurface singularities, and makes use of the recent work of Demailly and Kollár, AG/9…

Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action

We classify those manifolds mentioned in the title which have finite topological type. Namely we show any such connected M is isomorphic to a hyperkaehler quotient of a flat quaternionic vector space by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n-1 whose isometry group has rank n+1 is isometric to a 3-Sasakian quotient of a sphere by a torus. As a corollary, a compact connected quaternion-Kaehler 4n-manifold with positive scalar curvature and isometry group of rank n+1 is isometric to the quaternionic projective space or the …

Sasakian quiver gauge theories and instantons on cones over lens 5-spaces

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3)-equivariant solutions to the Hermitian Yang-Mills equations on the associated Calabi-Yau cones, and further compare them to…