JournalsrlmVol. 24, No. 3pp. 311–328

On Small-type formulae for curves in PSL(2,C(2, \mathbb C)

  • Emilio Musso

    Politecnico di Torino, Italy
  • Lorenzo Nicolodi

    Università di Parma, Italy
On Small-type formulae for curves in PSL$(2, \mathbb C$) cover
Download PDF


Taking the point of view of Legendrian curves in complex projective 3-space and using the classical Lie–Klein duality of algebraic geometry, we revisit various meromorphic representation formulae for Legendrian and null curves in PSL(2,C(2, \mathbb C. These include Small’s formula for null curves, the formulae for Legendrian curves given by Kokubu, Umehara and Yamada, by Gálvez, Martínez and Milán, and more recently by Ejiri and Takahashi. We discuss their relationships and provide a dictionary for their meromorphic data. Some examples related to the WW-curves of complex projective 3-space are discussed.

Cite this article

Emilio Musso, Lorenzo Nicolodi, On Small-type formulae for curves in PSL(2,C(2, \mathbb C). Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 24 (2013), no. 3, pp. 311–328

DOI 10.4171/RLM/656