Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality

Goo Ishikawa, Yoshinori Machida, and Masatomo Takahashi

Journal of Singularities
volume 3 (2011), 126-143

Received: 7 January 2011.

DOI: 10.5427/jsing.2011.3h

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We give the generic classification on singularities of tangent surfaces to Legendre curves and to null curves by using the contact-cone duality between the contact 3-sphere and the Lagrange-Grassmannian with cone structure of a symplectic 4-space. As a consequence, we observe that the symmetry on the lists of such singularities is breaking for the contact-cone duality, compared with the ordinary projective duality.


tangent developable, null curve, Legendre curve, Lagrangian-Grassmannian, projective structure, Engel structure

Mathematical Subject Classification:

Primary: 58K40; Secondary: 57R45, 53A20.

Author(s) information:

Goo Ishikawa, Yoshinori Machida Masatomo Takahashi
Department of Mathematics
Hokkaido University Numazu College of Technology Muroran Institute of Technology
Sapporo 060-0810, Japan Shizuoka 410-8501, Japan Muroran 050-8585, Japan
email: email: email: