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Differential-geometric methods are gaining increasing importance in
the understanding of a wide range of fundamental natural phenomena.
Very often, the starting point for such studies is a variational
problem formulated for a convenient Lagrangian. From a formal point
of view, a Lagrangian is a smooth real function defined on the
total space of the tangent bundle to a manifold satisfying some
regularity conditions. The main purpose of this book is to present:
(a) an extensive discussion of the geometry of the total space of a
vector bundle; (b) a detailed exposition of Lagrange geometry; and
(c) a description of the most important applications. New methods
are described for construction geometrical models for applications.
The various chapters consider topics such as fibre and vector
bundles, the Einstein equations, generalized Einstein--Yang--Mills
equations, the geometry of the total space of a tangent bundle,
Finsler and Lagrange spaces, relativistic geometrical optics, and
the geometry of time-dependent Lagrangians. Prerequisites for using
the book are a good foundation in general manifold theory and a
general background in geometrical models in physics. For
mathematical physicists and applied mathematicians interested in
the theory and applications of differential-geometric methods.
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."
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."
Differential-geometric methods are gaining increasing importance in
the understanding of a wide range of fundamental natural phenomena.
Very often, the starting point for such studies is a variational
problem formulated for a convenient Lagrangian. From a formal point
of view, a Lagrangian is a smooth real function defined on the
total space of the tangent bundle to a manifold satisfying some
regularity conditions. The main purpose of this book is to present:
(a) an extensive discussion of the geometry of the total space of a
vector bundle; (b) a detailed exposition of Lagrange geometry; and
(c) a description of the most important applications. New methods
are described for construction geometrical models for applications.
The various chapters consider topics such as fibre and vector
bundles, the Einstein equations, generalized Einstein--Yang--Mills
equations, the geometry of the total space of a tangent bundle,
Finsler and Lagrange spaces, relativistic geometrical optics, and
the geometry of time-dependent Lagrangians. Prerequisites for using
the book are a good foundation in general manifold theory and a
general background in geometrical models in physics. For
mathematical physicists and applied mathematicians interested in
the theory and applications of differential-geometric methods.
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