Finslerian Geometries

A Meeting of Minds

Inbunden, Engelska, 1999

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This work covers advances in Finslerian geometries, such as 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. It should 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.

Produktinformation

Utgivningsdatum1999-12-31
Mått155 x 235 x 23 mm
Vikt653 g
FormatInbunden
SpråkEngelska
SerieFundamental Theories of Physics
Antal sidor312
Upplaga2000
FörlagKluwer Academic Publishers
ISBN9780792361152

Tillhör följande kategorier

Matematisk fysik inom Naturvetenskap och teknik
Fysik inom Naturvetenskap och teknik
Biovetenskap inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Optimering inom Naturvetenskap och teknik

Section I. Pedagogy.- Generalizations of Finsler Geometry.- Finsler Geometry Inspired.- Finsler Geometry.- Section II. Summary and Overview.- Summary and Overview.- Section III. Meeting of Minds.- Some Remarks On the Conformal Equivalence of Complex Finsler Structures.- Deformations of Finsler Metrics.- The Constant Sprays of Classical Ecology and Noisy Finsler Perturbations.- On the Geometry of a Homogeneous Contact Transformation.- On Finsler Spaces of Douglas Type III.- Equations of Motion from Finsler Geometric Methods.- On the Theory of Finsler Submanifolds.- Finslerian Fields.- On the Inverse Problem of the Calculus of Variations for Systems of Second-Order Ordinary Differential Equations.- Complex Finsler Geometry Via the Equivalence Problem on the Tangent Bundle.- Lévy Concentration of Metric Measure Manifolds.- Hypersurfaces in Generalised Lagrange Spaces.- The Notion of Higher Order Finsler Space. Theory and Applications.- Generalized Complex Lagrange Spaces.- Gravity in Finsler Spaces.- Higher Order Ecological Metrics.- Area and Metrical Connections in Finsler Space.- Problem.- Finslerian Convexity and Optimization.- On Projective Transformations and Conformal Transformations of the Tangent Bundles of Riemannian Manifolds.

'aside from being well organized, typesetting of the book as well as proof reading is done very carefully. The layout is professional. The book deserves attention not only from mathematicians but also from natural scientists, especially for theoretical physics. It certainly helps to overcome such judges about Finsler Geometry like 'an impenetrable forest whose entire vegetation consists of tenors'or 'a jungle of tenors'. This book is highly readable and exciting.' Journal of Geodesy, 75:(5-6)(2001) 'It will be of interest to physicist and mathematicians whose work involves quantum field theory, general relativity and gravitation, programming and optimization. Mathematical biologist working in ecology and evolution will also find it useful.' General Relativity and Gravitation, 33:7 (2001) 'Aside from being well organized, typesetting of the book as well as proof reading is done very carefully. The layout is professional. Nevertheless, this book is highly readable and exciting.' Journal of Geodesy, 75:337-342 (2001)