I. A. Taimanov

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In the present article we examine in details global deformations of surfaces of revolution via the modified Korteweg–de Vries (mKdV) equations and the first integrals, of these deformations, regarded as invariants of surfaces. It is a sequel to our paper [8] where the general case of modified Novikov–Veselov (mNV) deformations is considered. Since the main(More)
A smooth manifold M is called symplectic if it carries a nondegenerate closed 2-form ω which is called a symplectic form. In this event a symplectic manifold means a pair (M,ω). Since the skew-symmetric form ω is nondegenerate, M is even-dimensional and moreover such manifold always carries an almost complex structure. Topology of symplectic manifolds is(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 ≥ 1 has been established in [19, 20] and this proof, in fact, works for spheres also. Being mostly interested in relations of these representations to the spectral theory and in(More)
In this paper we resume our study of the formality problem for symplectic manifolds, which we started in [1, 2] where the first examples of nonformal simply connected symplectic compact manifolds were constructed and a method of constructing such manifolds by symplectic blow-ups was introduced. A smooth manifold X is called symplectic if there is a(More)
(see Theorem 1 and Corollary 1). This generalizes the analogous result for tori in R which was proved by M.U. Schmidt and the first author (P.G.G.) [8] and confirmed the conjecture of the second author (I.A.T.) on the conformal invariance of the spectral curves of tori in R. Therewith by the spectral curve it was understood the analytic set M(Γ) in C formed(More)