7 citations · 14 across the 4 of their papers we have counts for
4 papers
Isothermic submanifolds of symmetric -spaces
F. E. Burstall, N. M. Donaldson, F. Pedit +1
We extend the classical theory of isothermic surfaces in conformal 3-space, due to Bour, Christoffel, Darboux, Bianchi and others, to the more general context of submanifolds of sy…
Isothermic hypersurfaces in R^{n+1}
Neil Donaldson, Chuu-Lian Terng
A diagonal metric sum_{i=1}^n g_{ii} dx_i^2 is termed Guichard_k if sum_{i=1}^{n-k}g_{ii}-sum_{i=n-k+1}^n g_{ii}=0. A hypersurface in R^{n+1} is isothermic_k if it admits line of c…
Conformally flat submanifolds in spheres and integrable systems
Neil Donaldson, Chuu-Lian Terng
E. Cartan proved that conformally flat hypersurfaces in S^{n+1} for n>3 have at most two distinct principal curvatures and locally envelop a one-parameter family of (n-1)-spheres.…
Generators for Rational Loop Groups and Geometric Applications
Neil Donaldson, Daniel Fox, Oliver Goertsches
Uhlenbeck proved that a set of simple elements generates the group of rational loops in GL(n,C) that satisfy the U(n)-reality condition. For an arbitrary complex reductive group, a…