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

1. Front Matter

   Pages i-xv

   PDF

2. Introductory Geometrical Background

   • P. L. Antonelli, R. S. Ingarden, M. Matsumoto

   Pages 1-31

3. Finsler Metrics

   • P. L. Antonelli, R. S. Ingarden, M. Matsumoto

   Pages 32-57

4. Connections in Finsler Spaces

   • P. L. Antonelli, R. S. Ingarden, M. Matsumoto

   Pages 58-96

5. Special Finsler Spaces

   • P. L. Antonelli, R. S. Ingarden, M. Matsumoto

   Pages 97-132

6. Finslerian Physics

   • P. L. Antonelli, R. S. Ingarden, M. Matsumoto

   Pages 133-200

7. Finslerian Biology

   • P. L. Antonelli, R. S. Ingarden, M. Matsumoto

   Pages 201-284

8. Back Matter

   Pages 285-311

   PDF

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 Contrary to these outdated fossilized opinions, we believe "the world is Finslerian" in a true sense and we will try to show this in our application in thermodynamics, optics, ecology,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.

• Finsler geometry
• Volume
• biology
• curvature
• differential geometry
• life sciences
• linear optimization
• mechanics
• optics
• thermodynamics

• Department of Mathematics, University of Alberta, Edmonton, Canada

  P. L. Antonelli

• Institute of Physics, N. Copernicus University, Toruń, Poland

  R. S. Ingarden

• Institute of Physics, University of Kyoto, Kyoto, Japan

  M. Matsumoto

Policies and ethics