Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A Differential Approach to GeometryElements of the Global Theory of Surfaces

A Differential Approach to Geometry: Elements of the Global Theory of Surfaces [Global theory of surfaces is interested in those properties which refer to wide pieces of the surface, not just to the neighborhood of each point. We study surfaces of revolution, ruled surfaces, developable surfaces. We study when two surfaces are just an “isometric deformation” of each other and establish the classification of developable surfaces. We pay special attention to the surfaces with constant Gaussian curvature and prove the Liebmann characterization of the sphere. We conclude with the study of polygonal decompositions, the Gauss–Bonnet theorem and the Euler–Poincaré characteristic.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Differential Approach to GeometryElements of the Global Theory of Surfaces

Download PDF
74 pages

Loading next page...
 
/lp/springer-journals/a-differential-approach-to-geometry-elements-of-the-global-theory-of-SzwG5y6eIq
Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2014
ISBN
978-3-319-01735-8
Pages
345 –418
DOI
10.1007/978-3-319-01736-5_7
Publisher site
See Chapter on Publisher Site

Abstract

[Global theory of surfaces is interested in those properties which refer to wide pieces of the surface, not just to the neighborhood of each point. We study surfaces of revolution, ruled surfaces, developable surfaces. We study when two surfaces are just an “isometric deformation” of each other and establish the classification of developable surfaces. We pay special attention to the surfaces with constant Gaussian curvature and prove the Liebmann characterization of the sphere. We conclude with the study of polygonal decompositions, the Gauss–Bonnet theorem and the Euler–Poincaré characteristic.]

Published: Aug 26, 2013

Keywords: Polygon Decomposition; Gauss Bonnet Theorem; Constant Gaussian Curvature; Developed Surface; Jordan Curve Theorem

There are no references for this article.