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Cayley's surface revisited

Hans Havlicek

Abstract

Cayley's (ruled cubic) surface carries a three-parameter family of twisted cubics. We describe the contact of higher order and the dual contact of higher order for these curves and show that there are three exceptional cases.

Cayley's surface revisited

Abstract

Cayley's (ruled cubic) surface carries a three-parameter family of twisted cubics. We describe the contact of higher order and the dual contact of higher order for these curves and show that there are three exceptional cases.

Paper Structure

This paper contains 3 sections, 4 theorems, 12 equations.

Table of Contents

  1. Introduction
  2. Contact of higher order
  3. Dual contact of higher order

Key Result

Theorem 1

Distinct cubic parabolas $c_{\alpha,\beta,\gamma}$ and $c_{\,{\overline{\newline\alpha}},{\overline\beta},{\overline{\newline\gamma}}\,}$ on Cayley's ruled surface have

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4