| Differential Geometry of Spray and Finsler Spaces 2001 Edition Contributor(s): Zhongmin Shen (Author) |
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ISBN: 0792368681 ISBN-13: 9780792368687 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: March 2001 Annotation: This book is a comprehensive report of recent developments in Finsler geometry and Spray geometry. Riemannian geometry and pseudo-Riemannian geometry are treated as the special case of Finsler geometry. The geometric methods developed in this subject are useful for studying some problems arising from biology, physics, and other fields.Audience: The book will be of interest to graduate students and mathematicians in geometry who wish to go beyond the Riemannian world. Scientists in nature sciences will find the geometric methods presented useful. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Differential Equations - General - Mathematics | Applied |
| Dewey: 515.352 |
| LCCN: 2001029079 |
| Physical Information: 0.63" H x 6.14" W x 9.21" (1.23 lbs) 258 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |