The geometry of fronts

• 成果类型: Article
• 署名作者: Saji, Kentaro; Umehara, Masaaki; Yamada, Kotaro
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.169.491
• 发表日期: 2009
• 页码: 491-529
• 关键词: flat fronts; hyperbolic 3-space; gaussian curvature; SURFACES; SINGULARITIES; INFINITY

摘要

We shall introduce the singular curvature function on cuspidal edges of surfaces, which is related to the Gauss-Bonnet formula and which characterizes the shape of cuspidal edges. Moreover, it is closely related to the behavior of the Gaussian curvature of a surface near cuspidal edges and swallowtails.