Geometry of Pseudo-Finsler Submanifolds (Mathematics and its Applications Volume 527)

Bejancu, Aurel; Farran, Hani Reda

ISBN 10: 0792366646 / ISBN 13: 9780792366645

Published by Springer, 2000

In. Seller Inventory # ria9780792366645_new

Synopsis:

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).

Synopsis: This book begins with a new approach to the geometry of pseudo-Finsler manifolds. It also discusses the geometry of pseudo-Finsler manifolds and presents a comparison between the induced and the intrinsic Finsler connections. The Cartan, Berwald, and Rund connections are all investigated. Included also is the study of totally geodesic and other special submanifolds such as curves, surfaces, and hypersurfaces. The book will be of interest to researchers working on pseudo-Finsler geometry in general, and on pseudo-Finsler submanifolds in particular.

Bibliographic Details

Title: Geometry of Pseudo-Finsler Submanifolds (...
Publisher: Springer
Publication Date: 2000
Binding: Hardcover
Condition: New