On uniformization of complex manifolds : the role of connections / R.C. Gunning.

Includes bibliographical references.

Frontmatter -- PREFACE -- CONTENTS -- ʹ 1. Introduction -- ʹ 2. The group of k-jets and its Lie algebra -- ʹ 3. The pseudogroups defined by partial differential equations -- ʹ 4. The classification of tangentially transitive pseudogroups: algebraic aspects -- ʹ 5. The classification of tangentially transitive pseudogroups: analytic aspects -- ʹ 6. Pseudogroup structures and their associated connections -- ʹ 7. Complex analytic affine connections -- ʹ 8. Complex analytic projective connections -- ʹ 9. Complex analytic canonical connections -- ʹ 10. Complex flat canonical structures on surfaces -- ʹ 11. Complex affine structures on surfaces -- ʹ 12. Complex projective structures on surfaces -- Bibliography -- Backmatter.

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. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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