Ribaucour transformations of the Surfaces with constant positive Gaussian curvatures in the 3-dimensional Euclidean space
Commun. Korean Math. Soc. 2006 Vol. 21, No. 1, 165-175
Printed March 1, 2006
Joonsang Park
Dongguk University
Abstract : We associate the surfaces of constant Gaussian curvature $K=1$ with no umbilics to a subclass of the solutions of $O(4,1)/O(3)\times O(1,1)$-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, sinh-Gordon equation, $G/K$-system, flat connection, sphere congruence, Ribaucour transformation
MSC numbers : 57N35
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