WEAKLY COMPLETE WAVE FRONTS WITH ONE PRINCIPAL CURVATURE CONSTANT

• HONDA Atsufumi

  National Institute of Technology Miyakonojo College

Abstract

Murata and Umehara gave a classification of complete flat fronts in the Euclidean 3-space and proved their orientability. Here, a flat front is a flat surface (i.e., a surface where one of the principal curvatures is identically zero) with admissible singularities. In this paper,we investigate wave fronts where one of the principal curvatures is a non-zero constant. Although they are orientable in the regular surface case, there exist non-orientable examples. We classify weakly complete ones and derive their orientability.

Journal

• Kyushu Journal of Mathematics

  Kyushu Journal of Mathematics 70 (2), 217-226, 2016

  Faculty of Mathematics, Kyushu University

Keywords

• wave front
• weak completeness, where one of the principal curvatures is constant
• umbilic point
• orientability

Details

• CRID: 1390282680205038592
• NII Article ID: 130005421161
• DOI: 10.2206/kyushujm.70.217
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/70/2/70_217/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed