The theory of sprays and Finsler spaces with applications in physics and biology
The theory of sprays and Finsler spaces with applications in physics and biology
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DOI：
10.1007/978-94-015-8194-3
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发表时间：
1993
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影响因子：
--
通讯作者：
P. Antonelli
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文献类型：
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作者：
P. Antonelli
本书由两位数学家和一位物理学家撰写：一位专门研究芬斯勒几何的纯数学家(松本真本)，一位研究数学生物学的(彼得·安东内利)，以及一位专门研究信息热力学的数学物理学家(罗曼·英加登)。这本书的主要目的是介绍喷雾(路径空间)和芬斯勒空间的原理和方法，以及在物理和生命科学中的应用实例。我们的目标是写一本关于Finsler几何及其应用的入门书籍，达到相当高级的水平。它是专门为纯数学，科学和应用数学的研究生，但也应该感兴趣的纯粹的“Finslerist”谁希望看到他们的主题应用。在经历了70多年相对缓慢的发展后，芬斯勒几何现在是一门拥有大量定理和技术的现代学科，其数学内容可与现代微分几何的任何领域相媲美。现在是时候大声疾呼了，反对那些认为芬斯勒几何学由于其计算复杂性而只是微不足道的，实际上没有有趣的应用的人。与这些过时的僵化观点相反，我们相信“世界是真正意义上的芬斯勒”，我们将试图在热力学、光学、生态学、进化论和发育生物学的应用中展示这一点。另一方面，在学科的复杂性没有消失的情况下，现代束论方法大大增加了它的可理解性。
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 Contrary to these outdated fossilized opinions, we believe" the world is Finslerian" in a true sense and we will try to show this in our application in thermodynamics, optics, ecology,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.