Clifford lattices and a conformal generalization of Desargues' theorem

被引：2
|
作者：
King, A. D. [1 ]
Schief, W. K. [2 ,3 ]
机构：
[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England
[2] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia
[3] Australian Res Council, Ctr Excellence Math & Stat Complex Syst, Canberra, ACT, Australia
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2012年 / 62卷 / 05期
关键词：
Conformal geometry; Integrable systems; Desargues' theorem; Clifford's configuration; GEOMETRY;
D O I：
10.1016/j.geomphys.2011.12.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Lattices composed of Clifford point-circle configurations provide a geometric representation of the discrete Schwarzian KP (dSKP) equation. Based on an A(n) perspective on such lattices, it is shown that their integrability, and hence that of the dSKP equation, is a consequence of a conformal generalization of the classical Desargues theorem of projective geometry. (C) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码：1088 / 1096
页数：9
相关论文
共 50 条
  • [21] The Structure of n Harmonic Points and Generalization of Desargues' Theorems
    Thaqi, Xhevdet
    Aljimi, Ekrem
    MATHEMATICS, 2021, 9 (09)
  • [22] Observations on Desargues' and Pascal's theorem.
    Bottema, O
    MATHEMATISCHE ANNALEN, 1935, 111 : 68 - 70
  • [23] Generalization lattices
    Hamilton, HJ
    Hilderman, RJ
    Li, LC
    Randall, DJ
    PRINCIPLES OF DATA MINING AND KNOWLEDGE DISCOVERY, 1998, 1510 : 328 - 336
  • [24] CONFORMAL TRANSFORMATIONS AND CLIFFORD ALGEBRAS
    LOUNESTO, P
    LATVAMAA, E
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 79 (04) : 533 - 538
  • [25] The hyperbolic Desargues theorem in the Poincare model of hyperbolic geometry
    Andrica, Dorin
    Barbu, Catalin
    STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2013, 58 (04): : 431 - 435
  • [26] ON THE CLIFFORD THEOREM FOR SURFACES
    Sun, Hao
    TOHOKU MATHEMATICAL JOURNAL, 2012, 64 (02) : 269 - 285
  • [27] The desargues theorem to build matching graph for N images
    Chellali, R
    Maaoui, C
    Fontaine, JG
    2004 IEEE CONFERENCE ON ROBOTICS, AUTOMATION AND MECHATRONICS, VOLS 1 AND 2, 2004, : 416 - 421
  • [28] Two-valenced association schemes and the Desargues theorem
    Mitsugu Hirasaka
    Kijung Kim
    Ilia Ponomarenko
    Arabian Journal of Mathematics, 2020, 9 : 481 - 493
  • [29] THEOREM OF DESARGUES IN PLANES WITH ANALOGS TO EUCLIDEAN ANGULAR BISECTORS
    PHADKE, BB
    MATHEMATICA SCANDINAVICA, 1976, 39 (02) : 191 - 194
  • [30] DISTRIBUTIVE LATTICES AS A GENERALIZATION OF BROUWERIAN LATTICES
    KROGER, H
    DISCRETE MATHEMATICS, 1977, 20 (03) : 297 - 299
12345