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On the point of inflexion of a curve in a projective space

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The author establishes the projective differential geometry of a curve inS n at a point of inflexion by locating a certain pyramid of geometrical characterization and finding the canonical equations of the curve in terms or1/2 (n 2 −n−4)−1 projective invariants.

Literatur

  1. (1)

    E. Bompiani, Per lo studio proiettivo-differenziale delle singolarità, Boll. Un. Mat. Ital. (1) 5(1926), pp. 118–20.

  2. (2)

    B. Su,An extension of Bompiani's osculants for a plane curve with a singular point. Tòhoku Math. Journ., 45(1938), pp. 239–44,Projective differential geometry of singularities of plane curves, Journ. Chin. Math. Soc., 2(1940), pp. 139–51. The latter will be referied to as Su (2).

  3. (4)

    Cf. Su (2), p. 142.

  4. (5)

    Cf.B. Su,Contributions to the projective theory of curves in space of Ndimensions (2nd Memoir), Journ. Chin. Math. Soc., 2(1940), pp. 277–89.

  5. (7)

    Cf.Su (2), p. 148.

  6. (8)

    Cf.Su (2), p. 145.

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Su, B. On the point of inflexion of a curve in a projective space. Annali di Matematica 26, 177–197 (1947). https://doi.org/10.1007/BF02415376

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Keywords

  • Differential Geometry
  • Projective Space
  • Projective Invariant
  • Canonical Equation
  • Geometrical Characterization