The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology

1993
ISBN: 978-0-7923-2577-2
Verlag: Springer Netherlands

Buch, Englisch, Band 58, 312 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1420 g

Reihe: Fundamental Theories of Physics

The present book has been written by two mathematicians and one physicist: a pure mathematician specializing in Finsler geometry (Makoto Matsumoto), one working in mathematical biology (Peter Antonelli), and a mathematical physicist specializing in information thermodynamics (Roman Ingarden). The main purpose of this book is to present the principles and methods of sprays (path spaces) and Finsler spaces together with examples of applications to physical and life sciences. It is our aim to write an introductory book on Finsler geometry and its applications at a fairly advanced level. It is intended especially for graduate students in pure mathemat­ ics, science and applied mathematics, but should be also of interest to those pure "Finslerists" who would like to see their subject applied. After more than 70 years of relatively slow development Finsler geometry is now a modern subject with a large body of theorems and techniques and has math­ ematical content comparable to any field of modern differential geometry. The time has come to say this in full voice, against those who have thought Finsler geometry, because of its computational complexity, is only of marginal interest and with prac­ tically no interesting applications. Contrary to these outdated fossilized opinions, we believe "the world is Finslerian" in a true sense and we will try to show this in our application in thermodynamics, optics, ecology, evolution and developmental biology. On the other hand, while the complexity of the subject has not disappeared, the modern bundle theoretic approach has increased greatly its understandability.

Zielgruppe

Research

Autoren/Hrsg.

Antonelli, P. L.

Matsumoto, M.

Ingarden, Roman S.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Naturwissenschaften Biowissenschaften Biowissenschaften Meeres- und Süßwasserökologie
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Angewandte Optik
• Technische Wissenschaften Technik Allgemein Physik, Chemie für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Preface.- 0. Introductory Geometrical Background.- 1. Finsler Metrics.- 2. Connections in Finsler Spaces.- 3. Special Finsler Spaces.- 4. Finslerian Physics.- 5. Finslerian Biology.- References.