RIBAUCOUR TRANSFORMATIONS OF THE SURFACES WITH CONSTANT POSITIVE GAUSSIAN CURVATURES IN THE 3-DIMENSIONAL EUCLIDEAN SPACE

Title & Authors
RIBAUCOUR TRANSFORMATIONS OF THE SURFACES WITH CONSTANT POSITIVE GAUSSIAN CURVATURES IN THE 3-DIMENSIONAL EUCLIDEAN SPACE
PARK, Joon-Sang;

Abstract
We associate the surfaces of constant Gaussian curvature K = 1 with no umbilics to a subclass of the solutions of $\small{O(4,\;1)/O(3){\times}O(1,\;1)-system}$. From this correspondence, we can construct new K = 1 surfaces from a known K = 1 surface by using a kind of dressing actions on the solutions of this system.
Keywords
Gaussian curvature;shih-Gordon equation;G/K-system;flat connection;sphere congruence;Ribaucour transformation;
Language
English
Cited by
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