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Complex Spaces in Finsler, Lagrange and Hamilton Geometries

  • Book
  • © 2004

Overview

Authors:
  1. Gheorghe Munteanu

    1. Faculty of Mathematics and Informatics, “Transilvania” University of Braşov, Braşov, Romania

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xi
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  2. Complex Manifolds

    • Gheorghe Munteanu
    Pages 1-16

  3. Complex and holomorphic vector bundles

    • Gheorghe Munteanu
    Pages 17-30

  4. The geometry of holomorphic tangent bundle

    • Gheorghe Munteanu
    Pages 31-53

  5. Complex Finsler spaces

    • Gheorghe Munteanu
    Pages 55-90

  6. Complex Lagrange geometry

    • Gheorghe Munteanu
    Pages 91-140

  7. Hamilton and Cartan complex spaces

    • Gheorghe Munteanu
    Pages 141-197

  8. Complex Finsler vector bundles

    • Gheorghe Munteanu
    Pages 199-208

  9. Back Matter

    Pages 209-228
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Keywords

About this book

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.

Authors and Affiliations

  • Faculty of Mathematics and Informatics, “Transilvania” University of Braşov, Braşov, Romania

    Gheorghe Munteanu

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