Generalized DPW method and an application to isometric immersions of space forms

DOI10.1007/s00209-008-0367-9zbMath1167.37031arXivmath/0604247OpenAlexW3106106595MaRDI QIDQ1014231

David Brander, Josef F. Dorfmeister

Publication date: 27 April 2009

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604247

zbMATH Keywords

harmonic mapsymmetric spaceloop groupIwasawa decompositionisometric immersionDPW methodBirkhoff factorization

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) 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) Differential geometric aspects of harmonic maps (53C43) Differential geometry of symmetric spaces (53C35) Local submanifolds (53B25)

Related Items

Curved flats, pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms ⋮ On a relation between potentials for pluriharmonic maps and para-pluriharmonic maps ⋮ Timelike constant mean curvature surfaces with singularities ⋮ Loop group decompositions in almost split real forms and applications to soliton theory and geometry ⋮ Twistors, 4-symmetric spaces and integrable systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras
• A classification of involutive automorphisms of an affine Kac-Moody Lie algebra
• Harmonic maps into Lie groups (classical solutions of the chiral model)
• Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
• Weierstrass type representation of harmonic maps into symmetric spaces
• Group actions and deformations for harmonic maps
• Curved flats in symmetric spaces
• Curved flats and isothermic surfaces
• Pluriharmonic maps, loop groups and twistor theory
• Birkhoff decompositions and Iwasawa decompositions for loop groups
• Hamiltonian stationary Lagrangian surfaces in \(\mathbb{C}^2\)
• On the classification of constant mean curvature tori
• Isometric immersions of space forms and soliton theory
• Curved flats, pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms
• Initial value problems of the sine-Gordon equation and geometric solutions
• Isometric immersions of space forms in space forms
• Holomorphic representation of constant mean curvature surfaces in Minkowski space: consequences of non-compactness in loop group methods
• Actions of Loop Groups on Harmonic Maps
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Harmonic tori in spheres and complex projective spaces.
• Grassmann Geometries in Infinite Dimensional Homogeneous Spaces and an Application to Reflective Submanifolds
• k -symmetric AKS systems and flat immersions into spheres
• Weierstraß-type representation of affine spheres