Lie Geometry

The Lie Quadric figure

Courses at UCSD, LaJolla, California, USA - Fillmore and Springer

Jay P. Fillmore - University of California at San Diego
Arthur Springer - San Diego State University

Twenty two-hour lectures
   Spring 1988 - hand-written notes by Fillmore
   Spring 1990 - typed notes by Fillmore and Springer
   Spring 1992 - additions to Spring 1990 course

Two important references are in:
   The geometric vein, The Coxeter Festschrift,
   C. Davis, B. Grünbaum, and F.A. Sherk, eds., Springer, New York, 1981.
 * J.F. Rigby, The geometry of cycles and generalized Laguerre inversion, pp. 355-378.
   Mathematical Reviews (MathSciNet): MR661792   Zentralblatt MATH: 0499.51003
 * I.M. Yaglom, On the circular transformations of Möbius, Laguerre and Lie, pp. 345-353.
   Mathematical Reviews (MathSciNet): MR661791


1988 Fillmore
     Seminar on Lie Geometry
     Universidad Central de Venezuela

1993 Fillmore and Springer
     Informal Seminar on Lie Geometry
     University of California, San Diego


1977 Fillmore
     On Lie's Higher Sphere Geometry
     Colloquiun talk
     University of Minnesota, Minneapolis, Minnesota

1991 Fillmore and Springer (both are speakers)
     Old and New Euclidean Theorems from Lie Geometry.  I and II.
     AMS San Francisco, January 16

1994 Fillmore (speaker); Arthur Springer
     The Generalized Apollonius Contact Problem
     AMS Minneaolis, Minnesota, August
     transparencies - additional transparencies


1979 Fillmore
     On Lie's higher sphere geometry.
     Enseign. Math. (2) 25 (1979), no. 1-2, 77--114.
     MR0543553 (81f:53041)
     article  - seals - Swiss Electronic Acacdemic Library Service

1995 --------; Arthur Springer;
     Planar sections of the quadric of Lie cycles and their Euclidean interpretations.
     Geom. Dedicata 55 (1995), no. 2, 175--193. 
     MR1334212 (96j:51005)


2000     Fillmore and Springer
         Determining circles and spheres satifing conditions which generalize tangency

earlier  Fillmore and Springer
version  An algorithm for determining circles and spheres satisfying conditions which generalize tangency