東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Topological, differential and confor...

A'Campo, N.

FindBook

Google Book

Amazon

博客來

Topological, differential and conformal geometry of surfaces

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Topological, differential and conformal geometry of surfaces/ by Norbert A'Campo.
作者:	A'Campo, N.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	x, 284 p. :ill. (chiefly col.), digital ;24 cm.
內容註:	-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.
Contained By:	Springer Nature eBook
標題:	Surfaces. -
電子資源:	https://doi.org/10.1007/978-3-030-89032-2
ISBN:	9783030890322

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

Topological, differential and conformal geometry of surfaces[electronic resource] /by Norbert A'Campo. - Cham :Springer International Publishing :2021. - x, 284 p. :ill. (chiefly col.), digital ;24 cm. - Universitext,2191-6675. - Universitext..

-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.

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 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.

ISBN: 9783030890322

Standard No.: 10.1007/978-3-030-89032-2doiSubjects--Topical Terms:

522215
Surfaces.

LC Class. No.: QA649 / .A33 2021

Dewey Class. No.: 516.36

Topological, differential and conformal geometry of surfaces
LDR:03051nmm a2200337 a 4500 001 2253782
003 DE-He213
005 20211027063708.0
006 m d
007 cr nn 008maaau
008 220327s2021 sz s 0 eng d
020 $a 9783030890322 $q (electronic bk.)
020 $a 9783030890315 $q (paper)
024 7 $a 10.1007/978-3-030-89032-2 $2 doi
035 $a 978-3-030-89032-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA649 $b .A33 2021
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
072 7 $a PBMP $2 thema
082 0 4 $a 516.36 $2 23
090 $a QA649 $b .A168 2021
100 1 $a A'Campo, N. $q (Norbert) $3 3522318
245 1 0 $a Topological, differential and conformal geometry of surfaces $h [electronic resource] / $c by Norbert A'Campo.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a x, 284 p. : $b ill. (chiefly col.), digital ; $c 24 cm.
490 1 $a Universitext, $x 2191-6675
505 0 $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 $a 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 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.
650 0 $a Surfaces. $3 522215
650 0 $a Geometry, Riemannian. $3 519718
650 1 4 $a Differential Geometry. $3 891003
650 2 4 $a Algebraic Topology. $3 891269
650 2 4 $a Algebraic Geometry. $3 893861
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Universitext. $3 812115
856 4 0 $u https://doi.org/10.1007/978-3-030-89032-2
950 $a Mathematics and Statistics (SpringerNature-11649)