Geometry of Pseudo-Finsler Submanifolds
Seiten
2000
|
2000 ed.
Springer (Verlag)
978-0-7923-6664-5 (ISBN)
Springer (Verlag)
978-0-7923-6664-5 (ISBN)
Provides an approach to the geometry of pseudo-Finsler manifolds. This book discusses the geometry of pseudo-Finsler manifolds and presents a comparison between the induced and the intrinsic Finsler connections. It also investigates the Cartan, Berwald, and Rund connections.
Finsler geometry is the most natural generalization of Riemannian geo- metry. It started in 1918 when P. Finsler [1] wrote his thesis on curves and surfaces in what he called generalized metric spaces. Studying the geometry of those spaces (which where named Finsler spaces or Finsler manifolds) became an area of active research. Many important results on the subject have been brought together in several monographs (cf. , H. Rund [3], G. Asanov [1], M. Matsumoto [6], A. Bejancu [8], P. L. Antonelli, R. S. Ingar- den and M. Matsumoto [1], M. Abate and G. Patrizio [1] and R. Miron [3]) . However, the present book is the first in the literature that is entirely de- voted to studying the geometry of submanifolds of a Finsler manifold. Our exposition is also different in many other respects. For example, we work on pseudo-Finsler manifolds where in general the Finsler metric is only non- degenerate (rather than on the particular case of Finsler manifolds where the metric is positive definite). This is absolutely necessary for physical and biological applications of the subject.
Secondly, we combine in our study both the classical coordinate approach and the modern coordinate-free ap- proach. Thirdly, our pseudo-Finsler manifolds F = (M, M', F*) are such that the geometric objects under study are defined on an open submani- fold M' of the tangent bundle T M, where M' need not be equal to the entire TMo = TM/O(M).
Finsler geometry is the most natural generalization of Riemannian geo- metry. It started in 1918 when P. Finsler [1] wrote his thesis on curves and surfaces in what he called generalized metric spaces. Studying the geometry of those spaces (which where named Finsler spaces or Finsler manifolds) became an area of active research. Many important results on the subject have been brought together in several monographs (cf. , H. Rund [3], G. Asanov [1], M. Matsumoto [6], A. Bejancu [8], P. L. Antonelli, R. S. Ingar- den and M. Matsumoto [1], M. Abate and G. Patrizio [1] and R. Miron [3]) . However, the present book is the first in the literature that is entirely de- voted to studying the geometry of submanifolds of a Finsler manifold. Our exposition is also different in many other respects. For example, we work on pseudo-Finsler manifolds where in general the Finsler metric is only non- degenerate (rather than on the particular case of Finsler manifolds where the metric is positive definite). This is absolutely necessary for physical and biological applications of the subject.
Secondly, we combine in our study both the classical coordinate approach and the modern coordinate-free ap- proach. Thirdly, our pseudo-Finsler manifolds F = (M, M', F*) are such that the geometric objects under study are defined on an open submani- fold M' of the tangent bundle T M, where M' need not be equal to the entire TMo = TM/O(M).
1. Pseudo-Finsler Manifolds.- 2. Pseudo-Finsler Submanifolds.- 3. Special Immersions of Pseudo-Finsler Manifolds.- 4. Geometry of Curves in Finsler Manifolds.- 5. Pseudo-Finsler Hypersurfaces.- 6. Finsler Surfaces.- Basic Notations and Terminology.- References.
| Erscheint lt. Verlag | 31.10.2000 |
|---|---|
| Reihe/Serie | Mathematics and Its Applications ; 527 | Mathematics and Its Applications ; 527 |
| Zusatzinfo | IX, 244 p. |
| Verlagsort | Dordrecht |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-7923-6664-6 / 0792366646 |
| ISBN-13 | 978-0-7923-6664-5 / 9780792366645 |
| Zustand | Neuware |
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