论文标题
广义几何和几何宽松流量的差分计算
Differential calculus for generalized geometry and geometric Lax flows
论文作者
论文摘要
使用一类通用连接，我们描述了某些差异的复杂$ \左（\ tildeω^* _ {\ Mathbb {t}}}}（m），\ tilde {\ tilde {\ mathbb {d}}}}^{\ mathbb {\ mathb {t}}}}}} \ prient of $ and $ wedge^*属性，其中$ \ mathbb {t} m = t m \ oplus t^*m $是$ m $上的广义切线捆绑包。许多经典的几何概念扩展到$ \ mathbb {t} m $，例如通用连接的曲率张量。特别是，当$ \ mathbb {t} m $具有通用度量和确切的Courant代数结构时，我们描述了Levi-Civita连接的类似物。我们进一步描述了与Chern-Weil同态，Weitzenböck身份，Ricci流和Ricci Soliton，Hermitian-Einstein方程以及全体形态载体束的程度的类似物。此外，Ricci流被放入几何宽松流的背景中，这可能具有独立的关注。
Employing a class of generalized connections, we describe certain differential complices $\left(\tilde Ω^*_{\mathbb{T}}(M), \tilde{\mathbb{d}}^{\mathbb{T}}\right)$ constructed from $\wedge^* \mathbb{T} M$ and study some of their basic properties, where $\mathbb{T} M = T M \oplus T^*M$ is the generalized tangent bundle on $M$. A number of classical geometric notions are extended to $\mathbb{T} M$, such as the curvature tensor for a generalized connection. In particular, we describe an analogue to the Levi-Civita connection when $\mathbb{T} M$ is endowed with a generalized metric and a structure of exact Courant algebroid. We further describe in generalized geometry the analogues to the Chern-Weil homomorphism, a Weitzenböck identity, the Ricci flow and Ricci soliton, the Hermitian-Einstein equation and the degree of a holomorphic vector bundle. Furthermore, the Ricci flows are put into the context of geometric Lax flows, which may be of independent interest.
