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The Geometry of Hamilton and Lagrange Spaces

  • Book
  • © 2002

Overview

Authors:
  1. Radu Miron

    1. Al. I. Cuza University, Iasi, Romania

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  2. Dragos Hrimiuc

    1. University of Alberta, Edmonton, Canada

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  3. Hideo Shimada

    1. Hokkaido Tokai University, Sapporo, Japan

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  4. Sorin V. Sabau

    1. Tokyo Metropolitan University, Tokyo, Japan

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Part of the book series: Fundamental Theories of Physics (FTPH, volume 118)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XV
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  2. The geometry of tangent bundle

    Pages 1-30

  3. Finsler spaces

    Pages 31-61

  4. Lagrange spaces

    Pages 63-86

  5. The geometry of cotangent bundle

    Pages 87-118

  6. Hamilton spaces

    Pages 119-137

  7. Cartan spaces

    Pages 139-158

  8. The duality between Lagrange and Hamilton spaces

    Pages 159-187

  9. Symplectic transformations of the differential geometry of T*M

    Pages 189-218

  10. The dual bundle of a k-osculator bundle

    Pages 219-248

  11. Linear connections on the manifold T*2M

    Pages 249-269

  12. Generalized Hamilton spaces of order 2

    Pages 271-282

  13. Hamilton spaces of order 2

    Pages 283-306

  14. Cartan spaces of order 2

    Pages 307-321

  15. Back Matter

    Pages 323-344
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Keywords

About this book

The title of this book is no surprise for people working in the field of Analytical Mechanics. However, the geometric concepts of Lagrange space and Hamilton space are completely new. The geometry of Lagrange spaces, introduced and studied in [76],[96], was ext- sively examined in the last two decades by geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and U.S.A. Many international conferences were devoted to debate this subject, proceedings and monographs were published [10], [18], [112], [113],... A large area of applicability of this geometry is suggested by the connections to Biology, Mechanics, and Physics and also by its general setting as a generalization of Finsler and Riemannian geometries. The concept of Hamilton space, introduced in [105], [101] was intensively studied in [63], [66], [97],... and it has been successful, as a geometric theory of the Ham- tonian function the fundamental entity in Mechanics and Physics. The classical Legendre’s duality makes possible a natural connection between Lagrange and - miltonspaces. It reveals new concepts and geometrical objects of Hamilton spaces that are dual to those which are similar in Lagrange spaces. Following this duality Cartan spaces introduced and studied in [98], [99],..., are, roughly speaking, the Legendre duals of certain Finsler spaces [98], [66], [67]. The above arguments make this monograph a continuation of [106], [113], emphasizing the Hamilton geometry.

Authors and Affiliations

  • Al. I. Cuza University, Iasi, Romania

    Radu Miron

  • University of Alberta, Edmonton, Canada

    Dragos Hrimiuc

  • Hokkaido Tokai University, Sapporo, Japan

    Hideo Shimada

  • Tokyo Metropolitan University, Tokyo, Japan

    Sorin V. Sabau

Bibliographic Information

  • Book Title: The Geometry of Hamilton and Lagrange Spaces

  • Authors: Radu Miron, Dragos Hrimiuc, Hideo Shimada, Sorin V. Sabau

  • Series Title: Fundamental Theories of Physics

  • DOI: https://doi.org/10.1007/0-306-47135-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 2002

  • Hardcover ISBN: 978-0-7923-6926-4Published: 31 May 2001

  • Softcover ISBN: 978-1-4020-0352-3Published: 30 November 2001

  • eBook ISBN: 978-0-306-47135-3Published: 11 April 2006

  • Series ISSN: 0168-1222

  • Series E-ISSN: 2365-6425

  • Edition Number: 1

  • Number of Pages: XVI, 338

  • Topics: Differential Geometry, Applications of Mathematics

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