Tohoku Mathematical Journal

Deformation and applicability of surfaces in Lie sphere geometry

Emilio Musso and Lorenzo Nicolodi

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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.

Article information

Source
Tohoku Math. J. (2), Volume 58, Number 2 (2006), 161-187.

Dates
First available in Project Euclid: 22 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1156256399

Digital Object Identifier
doi:10.2748/tmj/1156256399

Mathematical Reviews number (MathSciNet)
MR2248428

Zentralblatt MATH identifier
1155.53306

Subjects
Primary: 53A40: Other special differential geometries
Secondary: 53C24: Rigidity results

Keywords
Legendre surfaces deformation of surfaces Lie-applicable surfaces Lie sphere geometry rigidity

Citation

Musso, Emilio; Nicolodi, Lorenzo. Deformation and applicability of surfaces in Lie sphere geometry. Tohoku Math. J. (2) 58 (2006), no. 2, 161--187. doi:10.2748/tmj/1156256399. https://projecteuclid.org/euclid.tmj/1156256399


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