Various transformations of isothermic surfaces are discussed and their interrelations are analyzed. Applications to cmc-1 surfaces in hyperbolic space and their minimal cousins in Euclidean space are… (More)

We prove that any subset of ℝ2 parametrized by a C 1 periodic function and its derivative is the Euclidean invariant signature of a closed planar curve. This solves a problem posed by Calabi et al.… (More)

The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup–Kupershmidt… (More)

In this article we study constrained variational problems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the… (More)

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… (More)

We 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… (More)

We give an account of the construction of exterior different ial systems based on the notion of tableaux over Lie algebras as developed in [33]. Th e definition of a tableau over a Lie algebra is… (More)

In the present paper we study the Lie sphere geometry of Legendre surfaces by the method of moving frame and we prove an existence theorem for real-analytic Lie-minimal Legendre surfaces.

This volume contains lectures delivered at the International Conference “Curvature in Geometry" held in Lecce, Italy, 11-14 June, 2003 in honor of Professor Lieven Vanhecke. The name of Professor… (More)