Complex Spaces in Finsler, Lagrange and Hamilton Geometries

  • Gheorghe Munteanu

Part of the Fundamental Theories of Physics book series (FTPH, volume 141)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Gheorghe Munteanu
    Pages 1-16
  3. Gheorghe Munteanu
    Pages 17-30
  4. Gheorghe Munteanu
    Pages 31-53
  5. Gheorghe Munteanu
    Pages 55-90
  6. Gheorghe Munteanu
    Pages 91-140
  7. Gheorghe Munteanu
    Pages 141-197
  8. Gheorghe Munteanu
    Pages 199-208
  9. Back Matter
    Pages 209-228

About this book

Introduction

From a historical point of view, the theory we submit to the present study has its origins in the famous dissertation of P. Finsler from 1918 ([Fi]). In a the classical notion also conventional classification, Finsler geometry has besides a number of generalizations, which use the same work technique and which can be considered self-geometries: Lagrange and Hamilton spaces. Finsler geometry had a period of incubation long enough, so that few math­ ematicians (E. Cartan, L. Berwald, S.S. Chem, H. Rund) had the patience to penetrate into a universe of tensors, which made them compare it to a jungle. To aU of us, who study nowadays Finsler geometry, it is obvious that the qualitative leap was made in the 1970's by the crystallization of the nonlinear connection notion (a notion which is almost as old as Finsler space, [SZ4]) and by work-skills into its adapted frame fields. The results obtained by M. Matsumoto (coUected later, in 1986, in a monograph, [Ma3]) aroused interest not only in Japan, but also in other countries such as Romania, Hungary, Canada and the USA, where schools of Finsler geometry are founded and are presently widely recognized.

Keywords

Finsler geometry Volume curvature manifold quantum field theory

Authors and affiliations

  • Gheorghe Munteanu
    • 1
  1. 1.Faculty of Mathematics and Informatics“Transilvania” University of BraşovBraşovRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4020-2206-7
  • Copyright Information Springer Science+Business Media B.V. 2004
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6614-5
  • Online ISBN 978-1-4020-2206-7
  • About this book