Skip to main content
SpringerLink
Log in

Über die Finslerschen Räume mit Verallgemeinerter Metrik

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

Finsler spaces with generalized metric are defined as C∞ — manifolds, endowed with a Finslerian connection and a Finslerian tensor field of type (O,2). For this field, both the symmetric and the antisymmetric parts are non-degenerate, and the covariant h- and v-derivations vanish.

For these spaces the “Eisenhart problem” is solved, i.e. necessary and sufficient conditions for the existence, as well as the most general form of such a connection are determined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  1. BUCHNER, K.: On a new solution of Einstein's unified field theory. Progr. Theor. Phys.48 (1972) 1708–1717.

    Google Scholar 

  2. BUCHNER, K.: Energiekomplexe in der Einstein-Schrödinger Geometrie. Tensor N. S.,29 (1975) 267–273.

    Google Scholar 

  3. EINSTEIN, A.: A generalization of the relativistic theory of gravitation. Ann. Math.46 (1945) 578–584.

    Google Scholar 

  4. EISENHART, L.P.: Generalized Riemann Space. Proc. Nat. Acad. Sci. U.S.A.37 (1951) 5.

    Google Scholar 

  5. GHINEA, I.: Connexions finsleriennes presque symplectigues An. Univ. Timisoara, XV, fasc.2 (1977).

  6. MATSUMOTO, M.: The Theory of Finsler Connections. Publ. of the Study Group of Geometry, 5, College of Liberal Arts and Sci. Okayama Univ. Japan, 1970.

    Google Scholar 

  7. MIRON, R.: Asupra spatiilor Riemann generalizate. Com. St. Iasi (1969), 395–398.

  8. MIRON, R., Hashiguchi, M.: Metrical Finsler Connections. Rep. Fac. Sci. Kagoshima Univ. Japan, 1979, Nr. 12 (Math. Phys. chem.).

  9. OBATA, M.: Affine connections on Manifolds with Almost Complex, Quaternions or Hermitian Structure. Jap. Jour. Math.26 (1956) 48–77.

    Google Scholar 

  10. SCHRÖDINGER, E.: The final affine field laws I, II. Proc. Royal. Irish Academy,51 A (1945–48), 163–171, 205–216.

    Google Scholar 

  11. UTIYAMA, R.: Phys. Rev.101 (1956) 1597–1607.

    Article  Google Scholar 

  12. KIBBLE, T.W.B.: J. Math. Phys.2 (1961) 212–221.

    Article  Google Scholar 

  13. YANO, K.: Differential Geometry on Complex and Almost Complex Spaces. Pergamon Press, 1965.

Überblicksartikel

  1. HEHL F.W.: Spin und Torsion in der Allgemeinen Relativitätstheorie, Habilitationsschrift, Clausthal 1970. Vgl. auch General Relativity Gravitation4 (1973) 333–349 und5 (1974) 491–516.

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Geometrie Fakultät für Mathematik und Informatik, Universität Brasov, Rumänien

    Gheorghe Atanasiu

Authors
  1. Gheorghe Atanasiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Atanasiu, G. Über die Finslerschen Räume mit Verallgemeinerter Metrik. J Geom 19, 1–7 (1982). https://doi.org/10.1007/BF01930866

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01930866

Search

Navigation