Name: Finsler and Lagrange Geometries
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Author: P. L. Antonelli
ISBN: 9781402013904

Finsler and Lagrange Geometries

P. L. Antonelli

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In the last decade several international conferences on Finsler, Lagrange and Hamilton geometries were organized in Bra§ov, Romania (1994), Seattle, USA (1995), Edmonton, Canada (1998), besides the Seminars that periodically are held in Japan and Romania. All these meetings produced important progress in the field and brought forth the appearance of some reference volumes. Along this line, a new International Conference on Finsler and Lagrange Geometry took place August 26-31,2001 at the "Al.I.Cuza" University in Ia§i, Romania. This Conference was organized in the framework of a Memorandum of Un derstanding (1994-2004) between the "Al.I.Cuza" University in Ia§i, Romania and the University of Alberta in Edmonton, Canada. It was especially dedicated to Prof. Dr. Peter Louis Antonelli, the liaison officer in the Memorandum, an untired promoter of Finsler, Lagrange and Hamilton geometries, very close to the Romanian School of Geometry led by Prof. Dr. Radu Miron. The dedica tion wished to mark also the 60th birthday of Prof. Dr. Peter Louis Antonelli. With this occasion a Diploma was given to Professor Dr. Peter Louis Antonelli conferring the title of Honorary Professor granted to him by the Senate of the oldest Romanian University (140 years), the "Al.I.Cuza" University, Ia§i, Roma nia. There were almost fifty participants from Egypt, Greece, Hungary, Japan, Romania, USA. There were scheduled 45 minutes lectures as well as short communications.

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Cuprins

Section 1. Lagrange and Hamilton Geometry and Applications in Control.- Curvature tensors on complex Lagrange spaces.- Symplectic structures and Lagrange geometry.- A geometrical foundation for Seismic ray theory based on modern Finsler geometry.- On a problem of M. Matsumoto and Z. Shen.- Metrical homogeneous 2 — ? structures determined by a Finsler metric in tangent bundle.- Nonholonomic frames for Finsler spaces with (?, ?) metrics.- Invariant submanifolds of a Kenmotsu manifold.- The Gaussian curvature for the indicatrix of a generalized Lagrange space.- Infinitesimal projective transformations on tangent bundles.- Conformal transformations in Finsler geometry.- Induced vector fields in a hypersurface of Riemannian tangent bundles.- On a normal cosymplectic manifold.- The almost Hermitian structures determined by the Riemannian structures on the tangent bundle.- On the semispray of nonlinear connections in rheonomic Lagrange geometry.- ?dual complex Lagrange and Hamilton spaces.- Dirac operators on holomorphic bundles.- The generalised singular Finsler spaces.- n-order dynamical systems and associated geometrical structures.- The variational problem for Finsler spaces with (?, ?) — metric.- On projectively flat Finsler spheres (Remarks on a theorem of R.L. Bryant).- On the corrected form of an old result:necessary and sufficient conditions of a Randers space to be of constant curvature.- On the almost Finslerian Lagrange space of second order with (?, ?) metric.- Remarkable natural almost parakaehlerian structures on the tangent bundle.- Intrinsic geometrization of the variational Hamiltonian calculus.- Finsler spaces of Riemann-Minkowski type.- Finsler- Lagrange- Hamilton structures associated to control systems.- Preface Section 2.- Section 2.Applications to Physics.- Contraforms on pseudo-Riemannian manifolds.- Finslerian (?, ?)—metrics in weak gravitational models.- Applications of adapted frames to the geometry of black holes.- Implications of homogeneity in Miron’s sense in gauge theories of second order.- The free geodesic connection and applications to physical field theories.- The geometry of non-inertial frames.- Self-duality equations for gauge theories.