SPACE-LIKE ISOTHERMIC SURFACES AND GRASSMANNIAN SYSTEMS

We show that space-like isothermic surfaces in the pseudo-riemannian space Rn-j,j are associated to O(n - j+ 1, j + 1) / O(n - j,j) × O(1, 1)-system, and that the action of a rational map with two simple poles on the space of local solutions of O(n - j + 1, j + 1)/O(n - j,j) × O(1,1)-system correspo...

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Bibliographic Details
Published in:Tsukuba journal of mathematics 2006-06, Vol.30 (1), p.81-102
Main Author: Dussan, Martha P.
Format: Article
Language:English
Subjects:
Algebra
Curvature
Geometry
Mathematical surfaces
Mathematical vectors
Sine function
Solitons
Symmetry
Trivial solutions
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Summary:We show that space-like isothermic surfaces in the pseudo-riemannian space Rn-j,j are associated to O(n - j+ 1, j + 1) / O(n - j,j) × O(1, 1)-system, and that the action of a rational map with two simple poles on the space of local solutions of O(n - j + 1, j + 1)/O(n - j,j) × O(1,1)-system correspond to Ribaucour and Darboux transformations to space-like surfaces in Rn-j,j.
ISSN:0387-4982
DOI:10.21099/tkbjm/1496165030