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Transversality

  • Hubertus Th. Jongen
  • Peter Jonker
  • Frank Twilt
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 47)

Abstract

Let us consider in ℝ2 two smoothly embedded circles C 1, C 2 (i.e. C 1 and C 2 are manifolds in ℝ2 which are diffeomorphic to the circle S 1, cf. Fig. 7.1.1.a). C 1 and C 2 are called transversal at an intersection point \(\bar x\) if at this point they intersect under an angle unequal to 0 or π; more formally, this means: the tangent spaces of C 1, C 2 at \(\bar x\) span the whole ℝ2 (= space of embedding), cf. Fig. 7.1.1.b. In case of nontransversal intersection, the tangent spaces of C l and C 2 at the intersection point coincide, thus spanning a one-dimensional subspace of ℝ2 (Fig. 7.1.1.c).

Keywords

Tangent Space Dense Part Open Part Generic Subset Transversal Intersection 
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 2001

Authors and Affiliations

  • Hubertus Th. Jongen
    • 1
  • Peter Jonker
    • 2
  • Frank Twilt
    • 2
  1. 1.Department of MathematicsAachen University of TechnologyAachenGermany
  2. 2.Department of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands

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