Tangency

  • René Lavendhomme
Part of the Kluwer Texts in the Mathematical Sciences book series (TMS, volume 13)

Abstract

Let M be a microlinear object and m a point in M. Classically, a tangent vector at a point m in a differentiable manifold M can be described as an equivalence class of curves passing through m, two arcs being considered equivalent if their expressions in local coordinates have the same derivatives. But here, as we look at things in the infinitesimal — we are in the infinitesimal context — we can identify a tangent vector with an infinitesimal shifting, in other words with a “micro-arc” defined only on D.

Keywords

Vector Field Vector Bundle Basic Concept Tangent Vector Tangent Bundle 
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.

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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • René Lavendhomme
    • 1
  1. 1.Université Catholique de LouvainBelgium

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