%0 Journal Article %A Goo Ishikawa %A Yoshinori Machida, %A Masatomo Takahashi %T Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality %J Journal of Singularities %D 2011 %P 126-143 %V 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2011.3h/ %R 10.5427/jsing.2011.3h %F 10_5427_jsing_2011_3h