Differential Geometry of Spray and Finsler Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry of Spray and Finsler Spaces write by Zhongmin Shen. This book was released on 2013-03-14. Differential Geometry of Spray and Finsler Spaces available in PDF, EPUB and Kindle. In this book we study sprays and Finsler metrics. Roughly speaking, a spray on a manifold consists of compatible systems of second-order ordinary differential equations. A Finsler metric on a manifold is a family of norms in tangent spaces, which vary smoothly with the base point. Every Finsler metric determines a spray by its systems of geodesic equations. Thus, Finsler spaces can be viewed as special spray spaces. On the other hand, every Finsler metric defines a distance function by the length of minimial curves. Thus Finsler spaces can be viewed as regular metric spaces. Riemannian spaces are special regular metric spaces. In 1854, B. Riemann introduced the Riemann curvature for Riemannian spaces in his ground-breaking Habilitationsvortrag. Thereafter the geometry of these special regular metric spaces is named after him. Riemann also mentioned general regular metric spaces, but he thought that there were nothing new in the general case. In fact, it is technically much more difficult to deal with general regular metric spaces. For more than half century, there had been no essential progress in this direction until P. Finsler did his pioneering work in 1918. Finsler studied the variational problems of curves and surfaces in general regular metric spaces. Some difficult problems were solved by him. Since then, such regular metric spaces are called Finsler spaces. Finsler, however, did not go any further to introduce curvatures for regular metric spaces. He switched his research direction to set theory shortly after his graduation.
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 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology write by P.L. Antonelli. This book was released on 2013-03-09. The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology available in PDF, EPUB and Kindle. 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.
Frontiers In Differential Geometry, Partial Differential Equations And Mathematical Physics: In Memory Of Gu Chaohao
Frontiers In Differential Geometry, Partial Differential Equations And Mathematical Physics: In Memory Of Gu Chaohao - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Frontiers In Differential Geometry, Partial Differential Equations And Mathematical Physics: In Memory Of Gu Chaohao write by Mo-lin Ge. This book was released on 2014-03-18. Frontiers In Differential Geometry, Partial Differential Equations And Mathematical Physics: In Memory Of Gu Chaohao available in PDF, EPUB and Kindle. This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime.All contributors to this book are close friends, colleagues and students of Gu Chaohao. They are all excellent experts among whom there are 9 members of the Chinese Academy of Sciences. Therefore this book will provide some important information on the frontiers of the related subjects.
Lectures on Finsler Geometry
Lectures on Finsler Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Finsler Geometry write by Zhongmin Shen. This book was released on 2001. Lectures on Finsler Geometry available in PDF, EPUB and Kindle. In 1854, B Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P Finsler studied the variation problem in regular metric spaces. Around 1926, L Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world.Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory.
Differential Geometry And Its Applications - Proceedings Of The 10th International Conference On Dga2007
Differential Geometry And Its Applications - Proceedings Of The 10th International Conference On Dga2007 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry And Its Applications - Proceedings Of The 10th International Conference On Dga2007 write by Demeter Krupka. This book was released on 2008-07-14. Differential Geometry And Its Applications - Proceedings Of The 10th International Conference On Dga2007 available in PDF, EPUB and Kindle. This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture “Leonhard Euler — 300 years on” by R Wilson. Notable contributors include J F Cariñena, M Castrillón López, J Erichhorn, J-H Eschenburg, I Kolář, A P Kopylov, J Korbaš, O Kowalski, B Kruglikov, D Krupka, O Krupková, R Léandre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Muñoz Masqué, S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slovák, J Szilasi, L Tamássy, P Walczak, and others.
