Conformal invariant functionals of immersions of tori into \(\mathbb{R}^3\)

DOI10.1016/S0393-0440(97)00038-7zbMath0949.53007arXivdg-ga/9702015WikidataQ126844202 ScholiaQ126844202MaRDI QIDQ1299186

Martin Ulrich Schmidt, Petr G. Grinevich

Publication date: 25 June 2000

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/dg-ga/9702015

zbMATH Keywords

Dirac operatorWillmore functionalmodified Novikov-Veselov hierarchy

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25)

Related Items

Conformal maps from a 2-torus to the 4-sphere, Corrugated Surfaces with Slow Modulation and Quasiclassical Weierstrass Representation, Surfaces via spinors and soliton equations, The Weierstrass representation of closed surfaces in \(\mathbb{R}^3\), Generalized Weierstrass representation for surfaces in terms of Dirac-Hestenes spinor field, The Moutard transformation of two-dimensional Dirac operators and the conformal geometry of surfaces in four-dimensional space, Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori, Surfaces in the four-space and the Davey-Stewartson equations, Discrete holomorphic geometry I. Darboux transformations and spectral curves, The spectral curve of a quaternionic holomorphic line bundle over a 2-torus, On a discretization of asymptotic nets, The Moutard transformation of two-dimensional Dirac operators and Möbius geometry

Cites Work

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