1,721,323 research outputs found
Symplectic Applicability of Lagrangian Surfaces
Full text linkWe develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considere
Deformation and applicability of surfaces in Lie sphere geometry
No full textThe 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
Geometric Transformations on Null Curves in the Anti-de Sitter 3-Space
Full text linkWe provide a geometric transformation on null curves in the anti-de Sitter 3-space (AdS) which induces the Backlund transformation for the KdV equation. In addition, we show that this geometric transformation satisfies a suitable permutability theorem. We also illustrate how to implement it when the original null curve has constant bending
Laguerre geometry of surfaces with plane lines of curvature
No full textWe study surfaces with plane lines of curvature in the framework of Laguerre geometry and provide explicit representation formulae for these surfaces in terms of a potential function. As an application, we explicitly integrate all L-minimal surfaces with plane curvature lines
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