1990 - Course on Lie Geometry
University of Clifornia at San Diego
Notes by Fillmore and Springer
Course description
Location, prerequisites, brief information
Books on reserve in Science and Engineering Library
Suggestions for term-paper topics
Pages numbers displayed at left are those of the notes,
and only approximate the page numbers of the .pdf file.
Chapter 1. Introduction
2 Euclidean geometry
2 Apollonius contact problem
3 Preliminaries
7 Gergonne's construction
9 Möbius geometry
11 Facts about the inversive plane
12 The Arbelos of Pappus
14 Theorem of Miquel
15 Laguerre geometry
16 A recent theorem
19 Lie geometry
22 A non-trivial theorem
Chapter 2. Lie Cycles - Part A
2- 1 Cycles
2- 3 Relative power
2- 7 like and unlike
2- 9 touch
2-10 Some special cases
Chapter 2. Lie Cycles - Part B
2B- 1 Bunches
2B- 1 Provisional definition
2B- 3 Euclidean bunch
Point cycle bunch
Möbius bunch
Laguerre bunch
2B- 4 Lie bunch
2B- 5 "Seven pages of figures follow."
[Eight] pages of figures
2B- 6 Coördinates
2B- 7 The Lie quadric - preview
2B-10 Coda
Chapter 3. The Lie Quadric - Part A
3A- 1 The bilinear form
3A- 5 The quadric
3A- 7 Relation to the Eucidean plane
Figure 1 - The Lie quadric
3A- 9 Bunches of cycles
Figure 2 - Bunches
Figure 3 - Associated Laguerre cycle and Möbius circle
3A-11 Measurements
3A-12 Relative power
Chapter 3. The Lie Quadric - Part B
3B- 1 Aside on: off a quadric
3B- 2 Proposition [Yaglom]
3B- 4 The description of bunches due to Yaglom
3B- 4 Theorem (Yaglom)
3B- 4 Aside on: off a quadric (continued)
3B- 6 Proposition [Rigby]
3B- 7 Separation of cycles
3B- 8 The description of bunches due to Rigby
3B- 9 Theorem (Rigby)
3B- 9 Coördinates
3B-10 Types of bunches
3B-10 Lie bunches
3B-11 Möbius bunches
3B-13 Laguerre bunches
3B-15 Euclidean bunches
Concluding lecture - Notes by students
notes 1 notes 2
Miscellaneous notes by Fillmore and Springer
Fillmore Springer