A Contribution to the Vector and Tensor Analysis II

  • Zlatko Janković
Part of the International Centre for Mechanical Sciences book series (CISM, volume 6)


-In a previous paper [2] we developed the basic features of the vector and tensor analysis under the assumption that there is an n -dimensional vector space at every point of an m -dimensional parameter manifold. Here we make the final step to connect the vector spaces X(P), P ∈ Ω with the parameter manifold as far as possible. Such a manifold with a structure determined by the fundamental tensor and by the connection coefficients may be called a space. We therefore require the dimension m of the parameter manifold and the dimension n of the vector spaces X(P), P ∈ Ω to be equal, m = n Naturally, the results obtained for the case m not necessarily equal to n [2], when adapted to the case m = n remain conserved, while some new results and relations, characteristic of the case m = n, will be derived.


Basis Vector Curvature Tensor Riemann Space Torsion Tensor Antisymmetric Part 
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Copyright information

© Springer-Verlag Wien 1969

Authors and Affiliations

  • Zlatko Janković
    • 1
  1. 1.University of ZagrebCroatia

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