Finsler and Lagrange Geometries

by Anastasiei, Mihai; Antonelli, Peter L.

• ISBN13: 9781402013904
• ISBN10: 1402013906
• Format: Hardcover
• Copyright: 2003-12-01
• Publisher: Kluwer Academic Pub

Summary

This text gives the most recent results in Finsler and related geometries from the Miron school. Both pure and applied topics are covered. For example Higher-Order geometry, Hamilton and Cartan spaces, Legendre transformations, self-duality in Gauge fields, constant curvature spaces, Electromagnetics, Gravity theory, Black Holes, complex Finsler geometry and Finsler-Lagrange-Hamilton structures in control and optimization. There is also an article on Finsler Seismic ray theory which uses the software FINSLER based on MAPLE.

Table of Contents

Foreword	ix
Professor Peter Louis Antonelli at sixty	xi
Preface Section 1	xv
SECTION 1. LAGRANGE AND HAMILTON GEOMETRY AND APPLICATIONS IN CONTROL
Curvature tensors on complex Lagrange spaces
Aldea Nicoleta	3	(6)
Symplectic structures and Lagrange geometry
Mihai Anastasiei	9	(8)
A geometrical foundation for Seismic ray theory based on modern Finsler geometry
P.L. Antonelli, S.F. Rutz and M.A. Slawinski	17	(38)
On a problem of M. Matsumoto and Z.Shen
Sándor Bácsó	55	(8)
Metrical homogeneous 2 - π structures determined by a Finsler metric in tangent bundle
Victor Blanuta and B.T. Hassan	63	(6)
Nonholonomic frames for Finsler spaces with (α,β) metrics
Ioan Bucataru	69	(8)
Invariant submanifolds of a Kenmotsu manifold
Constantin Calin	77	(6)
The Gaussian curvature for the indicatrix of a generalized Lagrange space
Mircea Crasmareanu	83	(8)
Infinitesimal projective transformations on tangent bundles
Izumi Hasegawa and Kazunari Yamauchi	91	(8)
Conformal transformations in Finsler geometry
B.T. Hassan and Fatma Mesbah	99	(10)
Induced vector fields in a hypersurface of Riemannian tangent bundles
Masashi Kitayama	109	(4)
On a normal cosymplectic manifold
Ion Mihai and Radu Rosca	113	(6)
The almost Hermitian structures determined by the Riemannian structures on the tangent bundle
Radu Miron and Koji Matsumoto	119	(10)
On the semispray of nonlinear connections in rheonomic Lagrange geometry
Florian Munteams	129	(10)
L-dual complex Lagrange and Hamilton spaces
Gheorghe Munteanu	139	(10)
Dirac operators on holomorphic bundles
Ovidis Mumteamu	149	(6)
The generalised singular Finsler spaces
Tetsoya Nagano	155	(8)
n- order dynamical systems and associated geometrical structures
M. Neamtu and V. Obadeanu	163	(8)
The variational problem for Finsler spaces with (α,β) metric
Marcel Roman	171	(10)
On projectively flat Finsler spheres (Remarks on a theorem of R.L.Bryant)
Vasile Sorin Sabau	181	(12)
On the corrected form of an old result: necessary and sufficient conditions of a Randers space to be of constant curvature
Hideo Shimada and Vasile Sorin Sabáu	193	(4)
On the almost Finslerian Lagrange space of second order with (α,β) metric
Catalin Sterbeti and Brandusa Nicolaescu	197	(6)
Remarkable natural almost parakaehlerian structures on the tangent bundle
Emil Stoica	203	(10)
Intrinsic geometrization of the variational Hamiltonian calculus
Ovidiu Ilie Sandro	213	(12)
Finsler spaces of Riemann- Minkowski type
L. Tamássy	225	(8)
Finsler- Lagrange- Hamilton structures associated to control systems
Constantin Udriste	233	(12)
Preface Section 2	245	(4)
SECTION 2. APPLICATIONS TO PHYSICS
Contraforms on pseudo-Riemannian manifolds
M. Anastasiei, Gabriela Ciobanu and I. Gottlieb	249	(10)
Finslerian (α,β)- metrics in weak gravitational models
Vladimir Balan and Panayotis C. Stavrinos	259	(10)
Applications of adapted frames to the geometry of black holes
Livia Popescu	269	(8)
Implications of homogeneity in Miron's sense in gauge theories of second order
Adrian Sandovici	277	(10)
The free geodesic connection and applications to physical field theories
Thomas P. Storer	287	(16)
The geometry of non-inertial frames
Ion Sandru	303	(10)
Self duality equations for gauge theories
Gheorghe Zet and Vasile Manta	313