Topological, Differential and Conformal Geometry of Surfaces

Topological, Differential and Conformal Geometry of Surfaces
Author :
Publisher : Springer Nature
Total Pages : 282
Release :
ISBN-10 : 9783030890322
ISBN-13 : 3030890325
Rating : 4/5 (22 Downloads)

Book Synopsis Topological, Differential and Conformal Geometry of Surfaces by : Norbert A'Campo

Download or read book Topological, Differential and Conformal Geometry of Surfaces written by Norbert A'Campo and published by Springer Nature. This book was released on 2021-10-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Poincaré 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 Gauss–Bonnet 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 Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.


Topological, Differential and Conformal Geometry of Surfaces Related Books

Topological, Differential and Conformal Geometry of Surfaces
Language: en
Pages: 282
Authors: Norbert A'Campo
Categories: Mathematics
Type: BOOK - Published: 2021-10-27 - Publisher: Springer Nature

DOWNLOAD EBOOK

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 su
Geometry and Topology of Manifolds: Surfaces and Beyond
Language: en
Pages: 420
Authors: Vicente Muñoz
Categories: Education
Type: BOOK - Published: 2020-10-21 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with
Computational Conformal Geometry
Language: en
Pages: 324
Authors: Xianfeng David Gu
Categories: CD-ROMs
Type: BOOK - Published: 2008 - Publisher:

DOWNLOAD EBOOK

Introduction to Differential Geometry
Language: en
Pages: 426
Authors: Joel W. Robbin
Categories: Mathematics
Type: BOOK - Published: 2022-01-12 - Publisher: Springer Nature

DOWNLOAD EBOOK

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of
Mostly Surfaces
Language: en
Pages: 330
Authors: Richard Evan Schwartz
Categories: Mathematics
Type: BOOK - Published: 2011 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites in