Complex Differential Geometry
Complex Differential Geometry
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DOI：
10.1090/amsip/018
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发表时间：
2002-08
期刊：
影响因子：
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通讯作者：
F. Zheng
中科院分区：
文献类型：
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作者：
F. Zheng
复流形理论与数学的几个分支重叠，包括微分几何，代数几何，多复变量，整体分析，拓扑学，代数数论和数学物理。复流形提供了丰富的几何对象，例如任何一般复多项式集合的（公共）零轨迹总是复流形。然而，复流形的行为不同于一般的光滑流形;它们更连贯和脆弱。复流形的丰富而又限制性的特征使它们成为一个特殊而有趣的研究对象。这本书是一本独立的研究生教科书，讨论了复杂流形的微分几何方面。第一部分包含一般拓扑学、微分流形和基本黎曼几何的标准材料。第二部分讨论复流形与解析簇、层与全纯向量丛，并对曲面分类理论作了简要说明，为读者提供复流形的一些具体例子。
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classification theory, providing readers with some concrete examples of complex manifolds.