6 papers
Variationally complete actions on compact symmetric spaces
Claudio Gorodski, Gudlaugur Thorbergsson
We prove that an isometric action of a compact Lie group on a compact symmetric space is variationally complete if and only if it is hyperpolar.
Representations of compact Lie groups and the osculating spaces of their orbits
Claudio Gorodski, Gudlaugur Thorbergsson
Several classes of irreducible orthogonal representations of compact Lie groups that are of importance in Differential Geometry have the property that the second osculating spaces…
Completely integrable curve flows on Adjoint orbits
Chuu-Lian Terng, Gudlaugur Thorbergsson
It is known that the Schrödinger flow on a complex Grassmann manifold is equivalent to the matrix non-linear Schrödinger equation and the Ferapontov flow on a principal Adjoint U(n…
A global theory of flexes of periodic functions
Gudlaugur Thorbergsson, Masaaki Umehara
For a real valued periodic smooth function u on R, , one defines the osculating polynomial (of order 2n+1) at a point to be the unique trigonometric polynomi…
Cycles of Bott-Samelson type for taut representations
Claudio Gorodski, Gudlaugur Thorbergsson
Bott and Samuelson constructed explicit cycles representing a basis of the Z_2-homology of the orbits of variationally complete representations of compact Lie groups. As a conseque…
Sextactic points on a simple closed curve
Gudlaugur Thorbergsson, Masaaki Umehara
We give optimal lower bounds for the number of sextactic points on a simple closed curve in the real projective plane. Sextactic points are after inflection points the simplest pro…