Complex Differential Geometry

Front Cover
American Mathematical Society, 2000 - Mathematics - 264 pages
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.

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Metric Connection and Curvature
The Geometry of Complete Riemannian Manifolds
Complex manifolds and Analytic Varieties

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