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Topological, Differential and Conformal Geometry of Surfaces (Universitext) free ebook download

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Mathematics

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Author(s):	Norbert A'Campo

Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	3030890317
Pages:	296	OCR:		Quality:		ISBN13:
Uploader:	stirkout	Upload Date:	9/19/2022 7:42:44 PM

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This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincar Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the GaussBonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chows Theorem on compact holomorphic submanifolds in complex projective spaces.

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3147460	Book	https://nitroflare.com/view/F91F25A777C0...		0.00	stirkout

Tags: Conformal Differential Geometry Surfaces Topological Universitext

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Topological, Differential and Conformal Geometry of Surfaces (Universitext) free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics