• Communications of the Korean Mathematical Society
• /
• v.21 no.4
• /
• pp.739-747
• /
• 2006

By using O(m+n, 1)/$O(m){\times}O(n,1)-system$, we give an analytic version of Ribaucour transformation for flat m-dimensional submanifolds in $\mathbb{H}^{m+n}$ with flat, non-degenerate normal bundle and free of weak umbilics, where $n{\geq}m-1$.

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1577-1590
• /
• 2008

We study Ribaucour transformations on nondegenerate local isometric immersions of Lorentzian space forms into Lorentzian space forms with the same sectional curvatures which have flat normal bundles. They can be associated to dressing actions on the solution space of Lorentzian Grassmannian systems.

• Communications of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.165-175
• /
• 2006

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.