The present article is a sequel to [19, 20]. The results presented here extend onto general surfaces the results obtained in [20] for surfaces of revolution and were exposed in a lot of talks of theâ€¦ (More)

In this paper we resume our study of the formality problem for sym-plectic manifolds, which we started in [1, 2] where the first examples of nonformal simply connected symplectic compact manifoldsâ€¦ (More)

In the present article we consider Weierstrass representations of spheres in R. An existence of a global Weierstrass representation for any compact oriented surface of genus g â‰¥ 1 has beenâ€¦ (More)

A smooth manifold M is called symplectic if it carries a nondegenerate closed 2-form Ï‰ which is called a symplectic form. In this event a symplectic manifold means a pair (M,Ï‰). Since theâ€¦ (More)

It is shown that the equation which describes constant mean curvature surfaces via the generalized Weierstrassâ€“Enneper inducing has Ha-miltonian form. Its simplest finiteâ€“dimensional reduction is theâ€¦ (More)

such that i) the geodesic flow on MA is (Liouville) integrable by C âˆž first integrals; ii) the geodesic flow on MA is not (Liouville) integrable by real-analytic first integrals; iii) the topologicalâ€¦ (More)

In the present article we examine in details global deformations of surfaces of revolution via the modified Kortewegâ€“de Vries (mKdV) equations and the first integrals, of these deformations, regardedâ€¦ (More)

A new approach is proposed for study structure and properties of the total squared mean curvature W of surfaces in R 3. It is based on the generalized Weierstrass formulae for inducing surfaces. Theâ€¦ (More)

The Weierstrass representation for surfaces in R3 [8, 13] was generalized for surfaces in R4 in [12] (see also [4]). This paper uses the quaternion language and the explicit formulas for such aâ€¦ (More)