Related papers: Surfaces via spinors and soliton equations

The infinite many symmetries of Davey-Stewartson (DS) system are closely connected to the integrable deformations of surfaces in a four-dimensional space. In this paper, we give a direct algorithm to construct the expression of the DS…

We give a conformal representation in terms of meromorphic data for a certain class of spacelike surfaces in the Lorentz-Minkowski 4-space L^4 whose mean curvature vector is either lightlike or zero at each point. This representation…

We introduce two basic invariant forms which define generic surface in 3-space uniquely up to Lie sphere equivalence. Two particularly interesting classes of surfaces associated with these invariants are considered, namely, the Lie-minimal…

Demoulin surfaces in real projective $3$-space are investigated. Our result enable us to establish a generalized Weierstrass type representation for definite Demoulin surfaces by virtue of primitive maps into a certain semi-Riemannian…

By introducing generalized Backlund Transformations depending on arbitrary functions, wave and localized soliton solutions of the Davey- Stewartson equations are generated. Moreover explicit soliton solutions of the Hamiltonian DSI and…

Playing off against each other the real and complex structures, we elucidate the local structure of certain representation spaces in the world of Poisson geometry. Particular cases of these spaces arise as moduli spaces of semistable…

The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan, which treats a spin structure on a Riemann surface M as a complex line bundle S whose square is the…

We establish what semi-discrete linear Weingarten surfaces with Weierstrass-type representations in $3$-dimensional Riemannian and Lorentzian spaceforms are, confirming their required properties regarding curvatures and parallel surfaces,…

In this paper, the Weierstrass technique for harmonic maps S^2 -> CP^(N-1) is employed in order to obtain surfaces immersed in multidimensional Euclidean spaces. It is shown that if the CP^(N-1) model equations are defined on the sphere S^2…

We present a twistor description for null two-surfaces (null strings) in 4D Minkowski space-time. The Lagrangian density for a variational principle is taken as a surface-forming null bivector. The proposed formulation is reparametrization…

Recently I proposed a new calculation scheme of a partition function of an immersion object using path integral method and theory of soliton (to appear in J.Phys.A). I applied the scheme to problem of elastica in two-dimensional space and…

We have established a 1-1 correspondence between a solution of the universal Whitham hierarchy and a twistor space. The twistor space consists of a complex surface and a family of complex curves together with a meromorphic 2-form. The…

We show that isothermic surfaces and S-Willmore surfaces are also the solutions to the corresponding Blaschke's problem for both spacelike and timelike surfaces in pseudo-Riemannian space forms. For timelike surfaces both Willmore and…

Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete Weierstrass-type representations of certain surface classes…

We present a computational approach to general hyperelliptic Riemann surfaces in Weierstrass normal form. The surface is either given by a list of the branch points, the coefficients of the defining polynomial or a system of cuts for the…

For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the…

We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a far more complete theory than one would expect from general…

Relation between generalized Weierstrass representation for conformal immersion of generic surfaces into three-dimensional space and Lax-Phillips scattering theory for automorphic functions is considered.

In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the twistor projection of…

Minimal surfaces of general type in Euclidean 4-space are characterized with the conditions that the ellipse of curvature at any point is centered at this point and has two different principal axes. Any minimal surface of general type…