June Lester - Curriculum Vitae - Home

Mathematical Publications

Note: some of the papers listed below appear in more than one section. There are 39 distinct papers. Follow the links to see papers on |

Spacetime Geometry |

Both of the previous topics come together here: the simplest spacetime, Minkowski spacetime is an example of a metric vector space, while Alexandrov's theorem characterizes its transformations (Lorentz transformations) by the fact that they preserve pairs of points connected by light signals. Another example: Zeeman's theorem characterizes the causality-preserving transformations of Minkowski spacetime, for example. I've done generalizations of these and other theorems for several other spacetimes. In another, disjoint spacetime direction, my favourite paper |

The Beckman-Quarles Theorem in Minkowski Space
for a Spacelike Square-Distance.
Arch. Math. (Basel) |

Alexandrov-type Transformations on Einstein's
Cylinder Universe. C.
R. Math.Rep. Acad. Sci. Canada |

Transformations of Robertson-Walker Spacetimes
Preserving Separation Zero. Aequationes Math. |

A Physical Characterization of Conformal Transformations
of Minkowski Spacetime. Ann. Discrete Math. |

Conformal Minkowski Spacetime I: Relative Infinity
and Proper Time. Il
Nuovo Cimento |

Conformal Minkowski Spacetime II: A Cosmological
Model. Il Nuovo
Cimento |

Separation Preserving Transformations of de Sitter
Spacetime. Abh.
Math. Sem. Univ. Hamburg |

The Causal Automorphisms of de Sitter and Einstein
Cylinder Spacetimes.
J. Math. Phys. |

Relative Infinity in Projective de Sitter Spacetime
and its Relation to Proper Time. Ann. Discrete Math. |

Zeeman's Lemma on Robertson-Walker Spacetimes. J. Math. Phys. |

The Effect of a Relative Infinity on Cosmological
Redshifts. Astrophysics
and Space Science |

Does
Matter Matter? Physics
Essays |

Complex Triangle and Polygon Geometry |

This topic began as a minor recreational problem
and expanded into a major research project. Basically what I've done
is to develop a rather productive complex cross ratio formalism for triangle
geometry. First, I use a single complex number, called |

Triangles I: Shape. Aequationes Math. |

Triangles II: Complex Triangle Coordinates. Aequationes Math. |

Triangles III: Complex Triangle Functions. Aequationes Math. |

A generalization of Napoleon's
Theorem to n-gons. C.
R. Math. Soc. Canada |

My triangles work has been extended
to other planes: see for example |

The discover of the circle that has come to be known as the Lester circle was one of many theorems in Triangles III. For details of this theorem and a bibliography of papers it has inspired, please see the Lester Circle website. |