Unlimited

Authorized users

Can lend chapters, not whole ebooks

Topological, differential and conformal geometry of surfaces / Norbert A'Campo.

9783030890322 (electronic bk.)
3030890325 (electronic bk.)
9783030890315
3030890317

Cham : Springer, [2021]

©2021

English

1 online resource : illustrations (chiefly color)

10.1007/978-3-030-89032-2 doi

QA649 .A33 2021

516.3/6

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 Poincare 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. 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.

Includes bibliographical references and index.

Access limited to authorized users.

text file
PDF

Online resource; title from PDF title page (SpringerLink, viewed November 4, 2021).

Universitext. 2191-6675

Online Resources > Ebooks
All Resources