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On Uniformization of Complex Manifolds

The Role of Connections (MN-22)

Robert C. Gunning

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

The classical uniformization theorem for Riemann surfaces and its recent extensions can be viewed as introducing special pseudogroup structures, affine or projective structures, on Riemann surfaces. In fact, the additional structures involved can be considered as local forms of the uniformizations of Riemann surfaces. In this study, Robert Gunning discusses the corresponding pseudogroup structures on higher-dimensional complex manifolds, modeled on the theory as developed for Riemann surfaces.

Originally published in 1978.

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Schlagwörter

Projection (linear algebra), Vector space, Unit (ring theory), Analytic continuation, Complex analysis, Elliptic operator, Subgroup, Explicit formulae (L-function), Tangent space, Complex Lie group, Algebraic torus, Kähler manifold, Complex dimension, Invertible matrix, Complex manifold, Riemann surface, Differential geometry, Theorem, Lie algebra, Tensor field, Partial differential equation, Quotient space (topology), General linear group, Symmetrization, Algebraic surface, Riemann–Roch theorem, Pseudogroup, Schwarzian derivative, Dimension (vector space), Linear space (geometry), Covariant derivative, Uniformization theorem, Complex torus, Sheaf (mathematics), Group homomorphism, Automorphic function, Topological manifold, Characterization (mathematics), Cohomology, Subalgebra, Complex vector bundle, Symmetric tensor, Mathematical analysis, Vector bundle, Analytic function, Affine transformation, Holomorphic function, Linear map, Algebraic variety, Complex multiplication, Homomorphism, Existential quantification, Invariant subspace, Differentiable function, Complex plane, Representation theory, Automorphism, Hausdorff space, Tensor product, Contraction mapping, Complex number, Lie algebra representation, Tangent bundle, Projective line, Differential form, Canonical bundle, Manifold, Differentiable manifold, Tensor, Affine connection