Higher transgressions of the Pfaffian

Transgression on Hyperkähler Manifolds and Generalized Higher Torsion Forms

We propose a generalization of the Hodge $dd_c$-lemma to the case of hyperkähler manifolds. As an application of this result we derive the global construction of the fourth order transgression of the Chern character forms of hyperholomorphic bundles over compact hyperkähler manifolds. At the second part of the paper we consider the fourth order transgression for the infinite dimensional bundle arising from local families of hyperkähler manifolds. We propose a local construction of the fourth order transgression of the Chern character form. We derive an explicit expression for arising hypertors…

On higher-dimensional Courant algebroids

We define the transgression functor which associates to a (higher-dimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle of the manifold.

从 (2, 3, 5)-几何到平坦 (4, 7)-几何的 Pfaffian 嵌入的刻画

A characterization of Pfaffian embeddings from (2, 3, 5)- into flat (4, 7)-geometries

本文研究了从 (2,3,5)-流形到 7 维辛空间的 Pfaffian 嵌入存在性问题，通过求解微分方程并利用关联的 Cartan 几何及高阶曲率，完整刻画了可嵌入流形的条件。

Huber 定理成立的流形

Manifolds for which Huber's Theorem holds

本文研究带点球上 $L^{n/2}$ 标量曲率可积的共形度量，揭示其体积密度与吹缩极限的刚性，并在四维证明 Ricci 曲率 $L^2$ 可积及 Gauss–Bonnet–Chern 公式，给出 Huber 定理成立的充要条件。