Periodica Mathematica Hungarica

, Volume 22, Issue 2, pp 107–113 | Cite as

Some properties of associated pseudoconnections

  • Z. Kovács


Pseudoconnections (or quasi connections) were defined as a generalization of linear connections by Y.-C. Wong in [14], and were developed mainly by Italian and Rumanian mathematicians.

The purpose of this paper is to study some properties of a special type of pseudoconnections: the so-called associated pseudoconnections oginirating from linear connections in a very simple manner. In §1 we give a necessary and sufficient condition for a pseudoconnection to be associated, the in §2 we study the geodesics of an associated pseudoconnection. This notion has an immediate application in Finsler geometry, this is the theme of §3. Some questions connecting the curvature of associated pseudoconnections were studied by the author in [7].


Simple Manner Linear Connection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Anastasiei andI. Popovici, An intrinsic characterization of Finsler connections,Proc. Nat. Sem. Finsler Spac. (Brasov) 1980, 1–39.MR 83c:53068Google Scholar
  2. [2]
    I.Candela, Geodetiche rispetto ad una pseudoconnessione di uno spazio fibrato vettoriale,Note di Mat 3 (1983), 131–140.MR 86f:53028MathSciNetGoogle Scholar
  3. [3]
    C.DiComite, Geodetiche rispetto ad una pseudoconnessione lineare su uno varieteá differenziabili,Le Mat. (Catania)30 (1975), 320–328,MR 86f:53028Google Scholar
  4. [4]
    M.Falcitelli and A. M.Pastore, Sulle pseudoconnessioni proiettivamente equivalenti,Ren. Mat. Roma 13 (1980) 115–113.MR 81m:53039MathSciNetGoogle Scholar
  5. [5]
    W.Greub, S.Halperin and R.Vanstone, Connections, Curvature and Cohomology, Vol. 2, Academic Press, New York-London (1973).Google Scholar
  6. [6]
    Z.Kovács, On the different definitions of Finsler-connections,Pub. Math. (Debrecen)34 (1987), 69–73.MR 89b:53108zbMATHGoogle Scholar
  7. [7]
    Z. Kovács, Relative curvature of pseudoconnection and curvature mappings of Finsler spaces,Proc. Nat. Sem. Finsler Lagrange Spac. (Brasov) (1988), in printGoogle Scholar
  8. [8]
    M. Matsumoto, Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press (1986).MR 88f:53111Google Scholar
  9. [9]
    M.Matsumoto, Paths in a Finsler space,J. Math. Kyoto Univ. 3 (1964), 305–318.MR 30:1481zbMATHMathSciNetGoogle Scholar
  10. [10]
    R. Miron, Vector bundles Finsler-geometry,Proc. Nat. Sem. Finsler Spac. (Brasov), (1983), 147–188.MR 85c:53110Google Scholar
  11. [11]
    R.Miron, Techniques of Finsler geometry in the theory of vector bundles,Acta Sci. Math. 49 (1985) 119–129.zbMATHMathSciNetGoogle Scholar
  12. [12]
    M.Popovici and M.Anastesiei, Sur les bases de la geometrie finslerienne,C. R. Acad. Sc. Paris 290 (1980), 807–810.MR 81e:53055Google Scholar
  13. [13]
    J.Szilasi and Z.Kovács, Pseudoconnections and Finsler-type connections,Coll. Math. Soc. János Bolyai,46 (1984), 1165–1184.MR 89c:53056Google Scholar
  14. [14]
    Y. -C.Wong, Linear connections and quasi connections on a differentable manifold,Tôhoku Math. J. 14 (1962), 48–63.MR 25:2547zbMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó 1991

Authors and Affiliations

  • Z. Kovács
    • 1
  1. 1.Bessenyei György Tanítóképző Matematika TanszékNyiregyházaHungary

Personalised recommendations