Ju l 1 99 9 Generalized Weierstrass representation for surfaces in multidimensional Riemann spaces
نویسنده
چکیده
Generalizations of the Weierstrass formulae to generic surface immersed into R 4 , S 4 and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.
منابع مشابه
M ay 1 99 8 Generalized Weierstrass representation for surfaces in multidimensional Riemann spaces
Generalizations of the Weierstrass formulae to generic surface immersed into R 4 , S 4 and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.
متن کاملWeierstrass representation for surfaces in multidimensional Riemann spaces
Generalizations of the Weierstrass formulae to generic surface immersed into R 4 , S 4 and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.
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Let X denote a compact Riemann surface of genus g > 1. At each point P~X, there is a sequence of g integers, l=71(P)<72(P)<. . .<Tg(P)<2g , called the Weierstrass gap sequence at P. A positive integer ~/is a Weierstrass gap at P if there exists a holomorphic differential on X with a zero of order 7 1 at P. A positive integer which is not a gap at P is called a nongap at P. The point P is called...
متن کاملInduced surfaces and their integrable dynamics. II. Generalized Weierstrass representations in 4D spaces and
Induced surfaces and their integrable dynamics. II. Generalized Weierstrass representations in 4D spaces and deformations via DS hierarchy. Abstract Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfa...
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تاریخ انتشار 1998