Chern-Weil theory and complex differential Geometry

任课教师:二木昭人
时间: 每周二、周四13:30-15:05, 2019-9-10 ~ 2019-12-5
地点:清华大学近春园西楼第一会议室

课程描述

The first half of this course is about basic study on connections, curvature and characteristic classes. We start with connections for vector bundles including Levi-Civita connection for Riemannian manifolds and Chern connection for Hermitian vector bundles. Then we turn to connections for general principal bundles and the theory of characteristic classes (Chern-Weil theory). In the second half of the course some recent topics on complex/Kähler geometry will be discussed.

预备知识

Basic knowledge on manifolds, Lie groups and Lie algebras.

参考资料

[1] S.Kobayashi and K.Nomizu, Foundations of Differential Geometry I, II, 1996, Wiley Classics Library.

[2] S.S.Chern, Complex manifolds without potential theory, Van Nostrand Math. Series, 1967.

[3] A.Futaki, Kähler-Einstein metrics and integral invariants.  Springer Lecture Notes, vol. 1314, 1988.

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