Tohoku Mathematical Journal
2006

June
SECOND SERIES VOL. 58, NO. 2

Tohoku Math. J.
58 (2006), 161-187

Title DEFORMATION AND APPLICABILITY OF SURFACES IN LIE SPHERE GEOMETRY

Author Emilio Musso and Lorenzo Nicolodi

(Received March 31, 2004, revised December 6, 2004)
Abstract. The theory of surfaces in Euclidean space can be naturally formulated in the more general context of Legendre surfaces into the space of contact elements. We address the question of deformability of Legendre surfaces with respect to the symmetry group of Lie sphere contact transformations from the point of view of the deformation theory of submanifolds in homogeneous spaces. Necessary and sufficient conditions are provided for a Legendre surface to admit non-trivial deformations, and the corresponding existence problem is discussed.

2000 Mathematics Subject Classification. Primary 53A40; Secondary 53C24.

Key words and phrases. Legendre surfaces, deformation of surfaces, Lie-applicable surfaces, Lie sphere geometry, rigidity.

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