This paper studies isometric immersions of space forms by means of a
hierarchy of finite dimensional integrable systems in Lax form on loop
algebras.Comment: 15 pages, latex2e, postscript available at
  http://www_sfb288.math.tu-berlin.de/preprints.htm

Ferus, Dirk

Pedit, Franz

English

arXiv

Ferus, D

Pedit, F

ScholarWorks@UMass Amherst

Isometric immersions of space forms and soliton theory

The study of isometric immersions of space forms into space forms is a classical problem of differential geometry. In its simplest form it arises as the study of surfaces in 3-space of constant (non-zero) Gaussian curvature. In this case the integrability condition reduces to the sin and sinh-Gordon equations. Due to the complicated structure of these equations one focused over the past decade

Dirk Ferus

Franz Pedit

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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.76.745

Isometric Immersions of Space Forms and Soliton Theory

Isometric Immersions of Space Forms and Soliton Theory

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