标题： 卡拉比-丘流形导论 显示英文标题

标题： An Introduction to Calabi-Yau Manifolds

摘要： 本文的目标是通过引用李双代数理论，发展具有可积拟厄米向量丛结构的Courant代数胚理论。我们考虑底流形具有几乎拟复结构的情况，并利用此定义拟全纯代数胚的概念。我们研究拟全纯代数胚上的连接，并确定它们在何种适当意义上可以是拟复的。最后，我们通过一系列例子展示，具有拟复连接的精确拟全纯代数胚理论是拟凯勒几何和泊松-李群理论的推广。 显示英文摘要

摘要： The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost para-complex structure, and use this to define a notion of para-holomorphic algebroid. We investigate connections on para-holomorphic algebroids and determine an appropriate sense in which they can be para-complex. Finally, we show through a series of examples how the theory of exact para-holomorphic algebroids with a para-complex connection is a generalization of both para-K\"{a}hler geometry and the theory of Poisson-Lie groups.