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MARC 21

Topological, Differential and Conformal Geometry of Surfaces
Tag	Description
020	$a9783030890322$9978-3-030-89032-2
082	$a516.36$223
099	$aOnline resource: Springer
100	$aA'Campo, Norbert.$eauthor.$4aut$4http://id.loc.gov/vocabulary/relators/aut
245	$aTopological, Differential and Conformal Geometry of Surfaces$h[EBook] /$cby Norbert A'Campo.
250	$a1st ed. 2021.
260	$aCham :$bSpringer International Publishing :$bImprint: Springer,$c2021.
300	$aX, 284 p. 26 illus., 23 illus. in color.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aUniversitext,$x2191-6675
505	$a-1. Basic Differential Geometry -- 2. The Geometry of Manifolds -- 3. Hyperbolic Geometry -- 4. Some Examples and Sources of Geometry -- 5. Differential Topology of Surfaces -- 6. Riemann Surfaces -- 7. Surfaces of Genus g = 0 -- 8. Surfaces with Riemannian Metric -- 9. Outline: Uniformization by Spectral Determinant -- 10. Uniformization by Energy -- 11. Families of Spaces -- 12. Functions on Riemann Surfaces -- 13. Line Bundles and Cohomology -- 14. Moduli Spaces and Teichmüller Spaces -- 15. Dimensions of Spaces of Holomorphic Sections -- 16. The Teichmüller Curve and its Universal Property -- 17. Riemann Surfaces and Algebraic Curves -- 18. The Jacobian of a Riemann Surface -- 19. Special Metrics on J-Surfaces -- 20. The Fundamental Group and Coverings -- A. Reminder: Topology -- References -- Index.
520	$aThis 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.
533	$nMode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
710	$aSpringerLink (Online service)
830	$aUniversitext,$x2191-6675
856	$uhttps://doi.org/10.1007/978-3-030-89032-2