Generalized Weierstrass representation for surfaces in multidimensional Riemann spaces

Abstract

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.

LaTeX, 20 pages, minor misprints corrected

References in corpus (2)

• Conformal invariant functionals of immersions of tori into R^3
• The Weierstrass representation of spheres in $R^3$, the Willmore numbers, and soliton spheres

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