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Differential GeometryBundles, Connections, Metrics and Curvature$
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Clifford Henry Taubes

Print publication date: 2011

Print ISBN-13: 9780199605880

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199605880.001.0001

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Complex manifolds

Complex manifolds

(p.245) 17 Complex manifolds
Differential Geometry

Clifford Henry Taubes

Oxford University Press

This chapter examines complex manifolds. It discusses some basics concerning holomorphic functions on ℂn; the definition of a complex manifold; first examples of complex manifolds; the Newlander-Nirenberg theorem; metrics and almost complex structures on TM; the almost Kähler 2-form; symplectic forms; Kähler manifolds; complex manifolds with closed almost Kähler form; and examples of Kähler manifolds.

Keywords:   complex manifold, Newlander-Nirenberg theorem, metrics, Kähler manifolds

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