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Annali di Matematica Pura ed Applicata

, Volume 88, Issue 1, pp 143–154 | Cite as

Union congruence in a subspace of a Finsler space

  • C. M. Prasad
Article

Summary

The union curves of a Riemannian space were studied bySpringer[8],Misra[2] andUpadhyay[9]. In a Finsler space, these curves have been studied byPrakash-Behari[4],Sinha[7],Mishra-Sinha[3] andSingh[6].

In the present paper, we wish to extend the concept of union curves in the Finsler space and as such the concept of union congruence has been discussed. The two types of union curves of the Finsler subspace are the particular cases of these curves. These are also generalization of union curves and union curvatures of a vector-field of Finsler space. It has also been shown that the λ-geodesics [5] are special case of these curves.

Keywords

Riemannian Space Union Curvature Finsler Space Union Congruence Union Curf 
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.

References

  1. [1]
    H. A. Eliopoulos,Subspaces of a generalised metric space, Can. J. Math. XI, No. 2 (1959), 235–255.MathSciNetGoogle Scholar
  2. [2]
    R. S. Mishra,Sur certaines curbes appartenant a un sous-espace d’un espace Riemannian, Bull. des Sciences Mathematiques, 19 (1952), 1–8.Google Scholar
  3. [3]
    R. S. Mishra andR. S. Sinha,Union curvature of a curve in Finsler space, Tensor (N. S), 16(2), (1965), 160–168.MathSciNetGoogle Scholar
  4. [4]
    N. Prakash andRambehari,Union curves and union curvatures, Nat. Inst. Sci., India, Jubilee Vol. (1960–61).Google Scholar
  5. [5]
    C. M Prasad,On Δ curvatures and Δ geodesic principal directions of a congruence in a Finsler space, comunicated for pubblication in Rev. Fac. Sci. Uni. Istambul.Google Scholar
  6. [6]
    U. P. Singh,Union curves and union curvatures, Ph. D. Thesis, Gorakhpur University (1967).Google Scholar
  7. [7]
    B. B. Sinha,Union curves, Ph. D. Thesis, Gorakpur University (1962).Google Scholar
  8. [8]
    C. E. Springer,Union curves of a hypersurface, Can. J. Math., 2 (1950), 457–460.zbMATHMathSciNetGoogle Scholar
  9. [9]
    M. D. Upadhyay,Union curves of a Riemannian space, Tensor (N.S.), 16, (1965), 93–96.zbMATHMathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1971

Authors and Affiliations

  • C. M. Prasad
    • 1
  1. 1.GorakhpurIndia

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