Differential geometry of surfaces and Heisenberg ferromagnets
The relation between differential geometry of surfaces and some Heisenberg ferromagnet models is considered.
math.DG↗
arXiv subjects
Kur. Myrzakul
Publications and source records attributed to Kur. Myrzakul.
A note on the generalized Weierstrass representation
The study of the relation between the Weierstrass inducing formulae for constant mean curvature surfaces and the completely integrable euclidean nonlinear sigma-model suggests a connection among integrable sigma -models in a background and other type of surfaces. We show how a generalization of the Weierstrass representation can be achieved and we establish a connection with the Weingarten surfaces. We suggest also a possible generalization for two-dimensional surfaces immersed in a flat space R^8 with Euclidean metric.
math.DG↗
Integrability of the Gauss-Codazzi-Mainardi equation in 2+1 dimensions
Integrability of the (2+1)-dimensional Gauss-Codazzi-Mainardi equation is considered. It is shown that this equation is the particular cases of the Yang-Mills-Higgs-Bogomolny and self-dual Yang-Mills equations.
math.DG↗
Notes on Riemann geometry and integrable systems. Part V
Some aspects of multidimensional soliton geometry are considered.
gr-qc↗
Notes on Riemann geometry and integrable systems. Part IV
The connection between multidimensional soliton equations and three-dimensional Riemann space is discussed.
gr-qc↗
Deformation surfaces, integrable systems and Chern - Simons theory
A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern-Simons action via reduction of the gauge connection in Hermitian symmetric spaces. In this paper we show that the methods developed in studying classical non-Abelian pure Chern-Simons actions, can be naturally implemented by means of a geometrical interpretation of such systems. The Chern-Simons equation of motion turns out to be related to time evolving 2-dimensional surfaces in such a way that these deformations are both locally compatible with the Gauss-Mainardi-Codazzi equations and completely integrable. The properties of these relationships are investigated together with the most relevant consequences. Explicit examples of integrable surface deformations are displayed and discussed.
nlin.SI↗
Soliton equations in N-dimensions as exact reductions of Self-Dual Yang-Mills equation IV. The mM-LXII and Bogomolny equations
Some aspects of the multidimensional soliton geometry are considered. The relation between soliton equations in 2+1 dimensions and the Self-Dual Yang-Mills and Bogomolny equations are discussed.
math-ph↗