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Translation Planes

Foundations and Construction Principles

  • Book
  • © 1995

Overview

Authors:
  1. Norbert Knarr
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1611)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-vi
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  2. Introduction

    • Norbert Knarr
    Pages 1-4

  3. Foundations

    • Norbert Knarr
    Pages 5-24

  4. Spreads of 3-dimensional projective spaces

    • Norbert Knarr
    Pages 25-39

  5. Kinematic spaces

    • Norbert Knarr
    Pages 40-47

  6. Examples and supplements

    • Norbert Knarr
    Pages 48-60

  7. Locally compact 4-dimensional translation planes

    • Norbert Knarr
    Pages 61-77

  8. Planes of Lenz type V with complex kernel

    • Norbert Knarr
    Pages 78-94

  9. Locally compact translation planes of higher dimension

    • Norbert Knarr
    Pages 95-103

  10. Back Matter

    Pages 104-113
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Keywords

About this book

The book discusses various construction principles for translation planes and spreads from a general and unifying point of view and relates them to the theory of kinematic spaces. The book is intended for people working in the field of incidence geometry and can be read by everyone who knows the basic facts about projective and affine planes.
The methods developed work especially well for topological spreads of real and complex vector spaces. In particular, a complete classification of all semifield spreads of finite dimensional complex vector spaces is obtained.

Bibliographic Information

  • Book Title: Translation Planes

  • Book Subtitle: Foundations and Construction Principles

  • Authors: Norbert Knarr

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0096310

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Softcover ISBN: 978-3-540-60208-8Published: 18 September 1995

  • eBook ISBN: 978-3-540-44724-5Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 122

  • Topics: Geometry

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