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 selfcontained 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. The last part is the main purpose of the book in it, the author discusses metrics, connections, curvature, and the various roles they play in the study of complex manifolds. A significant amount of exercises are provided to enhance student comprehension and practical experience.
About Fangyang Zheng
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Author  :  Fangyang Zheng 
Publisher  :  American Mathematical Society 
Data Published  :  15 January 2002 
ISBN  :  0821829602 
EAN  :  9780821829608 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  264 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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