Geometric invariants of 5/2-cuspidal edges

• Honda Atsufumi

  Department of Applied Mathematics Faculty of Engineering Yokohama National University

• Saji Kentaro

  Department of Mathematics Kobe University

抄録

We introduce two invariants called the secondary cuspidal curvature and the bias on 5/2-cuspidal edges, and investigate their basic properties. While the secondary cuspidal curvature is an analog of the cuspidal curvature of (ordinary) cuspidal edges, there are no invariants corresponding to the bias. We prove that the product (called the secondary product curvature) of the secondary cuspidal curvature and the limiting normal curvature is an intrinsic invariant. Using this intrinsicity, we show that any real analytic 5/2-cuspidal edges with non-vanishing limiting normal curvature admit non-trivial isometric deformations, which provides the extrinsicity of various invariants.

収録刊行物

• ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ

  ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ 42 (3), 496-525, 2019-10-31

  国立大学法人 東京工業大学理学院数学系

キーワード

• 5/2-cusp
• rhamphoid cusp
• 5/2-cuspidal edge
• frontal
• spacelike surface with constant mean curvature
• intrinsic invariant
• isometric deformation
• Kossowski metric

詳細情報

• CRID: 1390282752358554112
• NII論文ID: 130007742214
• DOI: 10.2996/kmj/1572487230
• ISSN: 18815472
• ISSN: 03865991
• 本文言語コード: en
• データソース種別:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用不可