Geometries on Surfaces

ISBN-13: 9780521660587 / Angielski / Twarda / 2002 / 514 str.

Burkard Polster; Gunther Stienke; Gunter Steinke

Opis

One century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have included detailed sections on what is known as well as outlining problems that remain to be solved. There are sections on classical geometries, methods for constructing non-classical geometries and classifications and characterizations of geometries. This work is related to a host of other fields including approximation, convexity, differential geometry topology and many more. This book will appeal to students, researchers and lecturers working in geometry or any one of the many associated areas outlined above.

Recenzje

'The main objective of the book, to give an intuitive and fairly complete picture of the wealth of geometries living on surfaces and of the beauty of the subject, has been accomplished in an excellent way. The text provides an easily accessible and well-motivated introduction to topological geometry.' Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts

Spis treści

1. Geometries for pedestrians; 2. Flat linear spaces; 3. Spherical circle planes; 4. Toroidal circle planes; 5. Cylindrical circle planes; 6. Generalized quadrangles; 7. Tubular circle planes; Appendices.