Finslerian Geometries

by Antonelli, Peter L.

• ISBN13: 9780792361152
• ISBN10: 0792361156
• Format: Hardcover
• Copyright: 2000-02-01
• Publisher: Kluwer Academic Pub

Summary

This text will acquaint the reader with the most recent advances in Finslerian geometries, i.e. anisotropic geometries, and their applications by the Japanese, European and American schools. It contains three introductory articles, one from each of these schools, giving a broad overview of basic ideas. Further papers treat topics from pure mathematics such as complex differential geometry, equivalence methods, Finslerian deformations, constant sprays, homogeneous contact transformations, Douglas spaces, submanifold theory, inverse problems, area theory, and more. This book completes the Kluwer trilogy on Finslerian Geometry by P.L. Antonelli and his associates. Audience: This volume will be of interest to physicists and mathematicians whose work involves quantum field theory, combination theory and relativity, programming and optimization. Mathematical biologists working in ecology and evolution will also find it useful.

Table of Contents

Preface	vii
SECTION I. PEDAGOGY	1	(24)
Generalizations of Finsler Geometry	3	(6)
M. Anastasiei
D. Hrimiuc
Finsler Geometry Inspired	9	(6)
L. Kozma
L. Tamassy
Finsler Geometry	15	(10)
H. Shimada
V.S. Sabau
SECTION II. SUMMARY AND OVERVIEW	25	(8)
Summary and Overview	27	(6)
P.L. Antonelli
SECTION III. MEETING OF MINDS	33	(264)
Some Remarks On the Conformal Equivalence of Complex Finsler Structures	35	(18)
T. Aikou
Deformations of Finsler Metrics	53	(14)
M. Anastasiei
H. Shimada
The Constant Sprays of Classical Ecology and Noisy Finsler Perturbations	67	(12)
P.L. Antonelli
On the Geometry of a Homogeneous Contact Transformation	79	(10)
P.L. Antonelli
D. Hrimiuc
On Finsler Spaces of Douglas Type III	89	(6)
S. Bacso
M. Matsumoto
Equations of Motion from Finsler Geometric Methods	95	(16)
R.G. Beil
On the Theory of Finsler Submanifolds	111	(20)
A. Bejancu
Finslerian Fields	131	(8)
H.E. Brandt
On the Inverse Problem of the Calculus of Variations for Systems of Second-Order Ordinary Differential Equations	139	(12)
M. Crampin
Complex Finsler Geometry Via the Equivalence Problem on the Tangent Bundle	151	(18)
J.J. Faran, V
Levy Concentration of Metric Measure Manifolds	169	(10)
W. Gu
Z. Shen
Hypersurfaces in Generalised Lagrange Spaces	179	(14)
M. Kitayama
The Notion of Higher Order Finsler Space. Theory and Applications	193	(16)
R. Miron
Generalized Complex Lagrange Spaces	209	(14)
G. Munteanu
Gravity in Finsler Spaces	223	(22)
S.F. Rutz
F.M. Paiva
Higher Order Ecological Metrics	245	(18)
V.S. Sabau
Area and Metrical Connections in Finsler Space	263	(18)
L. Tamassy
Problem	281	(2)
L. Tamassy
Finslerian Convexity and Optimization	283	(14)
C. Udriste
On Projective Transformations and Conformal Transformations of the Tangent Bundles of Riemannian Manifolds	297
K. Yamauchi