Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics) - Hardcover

Thorpe, John A.

Hardcover

ISBN 10: 3540903577 ISBN 13: 9783540903574

Verlag: Springer Berlin, 1994

Inhaltsangabe

This introductory text develops the geometry of n-dimensional oriented surfaces in Rn+1. By viewing such surfaces as level sets of smooth functions, the author is able to introduce global ideas early without the need for preliminary chapters developing sophisticated machinery. the calculus of vector fields is used as the primary tool in developing the theory. Coordinate patches are introduced only after preliminary discussions of geodesics, parallel transport, curvature, and convexity. Differential forms are introduced only as needed for use in integration. The text, which draws significantly on students' prior knowledge of linear algebra, multivariate calculus, and differential equations, is designed for a one-semester course at the junior/senior level. TOC: Contents: Graphs and Level Sets.- Vector Fields.- The Tangent Space.- Surfaces.- Vector Fields on Surfaces; Orientation.- The Gauss Map.- Geodesics.- Parallel Transport.- The Weingarten Map.- Curvature of Plane Curves.- Arc Length and Line Integrals.- Curvature of Surfaces.- Convex Surfaces.- Parametrized Surfaces.- Local Equivalence of Surfaces and Parametrized Surfaces.- Focal Points.- Surface Area and Volume.- Minimal Surfaces.- The Exponential Map.- Surfaces with Boundary.- The Gauss-Bonnet Theorem.- Rigid Motions and Congruence.- Isometries.- Riemannian Metrics.

Details zur Ausgabe

• Verlag: Springer Berlin
• Erscheinungsdatum: 1994
• Sprache: Englisch
• ISBN 10: 3540903577
• ISBN 13: 9783540903574
• Einband: Gebundene Ausgabe
• Auflage: 4
• Anzahl der Seiten: 280
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland