Cassini Curves in Normed Planes

被引：3
|
作者：
Martini, Horst [1 ]
Wu, Senlin [2 ]
机构：
[1] Tech Univ Chemnitz, Fac Math, D-09107 Chemnitz, Germany
[2] Harbin Univ Sci & Technol, Dept Appl Math, Harbin 150080, Peoples R China
来源：
RESULTS IN MATHEMATICS | 2013年 / 63卷 / 3-4期
关键词：
Bisector; Cassini curve; lower semi-inner products; Minkowski plane; normed plane; upper semi-inner products; SPACES;
D O I：
10.1007/s00025-012-0260-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We extend the concept of Cassini curves from the Euclidean plane to normed (or Minkowski) planes and show that geometric properties of (Minkowskian) Cassini curves are closely related to geometric properties of the unit disc determining the underlying normed plane.
引用
收藏
页码：1159 / 1175
页数：17
相关论文
共 50 条
  • [1] Cassini Curves in Normed Planes
    Horst Martini
    Senlin Wu
    [J]. Results in Mathematics, 2013, 63 : 1159 - 1175
  • [2] On Zindler Curves in Normed Planes
    Martini, Horst
    Wu, Senlin
    [J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2012, 55 (04): : 767 - 773
  • [3] ON LEGENDRE CURVES IN NORMED PLANES
    Balestro, Vitor
    Martini, Horst
    Teixeira, Ralph
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 2018, 297 (01) : 1 - 27
  • [4] Geometric dilation of closed curves in normed planes
    Martini, Horst
    Wu, Senlin
    [J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2009, 42 (04): : 315 - 321
  • [5] HALVING CLOSED CURVES IN NORMED PLANES AND RELATED INEQUALITIES
    He, Chan
    Martini, Horst
    Wu, Senlin
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2009, 12 (04): : 719 - 731
  • [6] ON BISECTORS IN NORMED PLANES
    Jahn, Thomas
    Spirova, Margarita
    [J]. CONTRIBUTIONS TO DISCRETE MATHEMATICS, 2015, 10 (02) : 1 - 9
  • [7] Concepts of curvatures in normed planes
    Balestro, Vitor
    Martini, Horst
    Shonoda, Emad
    [J]. EXPOSITIONES MATHEMATICAE, 2019, 37 (04) : 347 - 381
  • [8] On Reduced Triangles in Normed Planes
    Alonso, Javier
    Martini, Horst
    Spirova, Margarita
    [J]. RESULTS IN MATHEMATICS, 2013, 64 (3-4) : 269 - 288
  • [9] Observations on circumcenters in normed planes
    Väisälä J.
    [J]. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2017, 58 (3): : 607 - 615
  • [10] Slopes of bisectors in normed planes
    Väisälä J.
    [J]. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2013, 54 (1): : 225 - 235
12345