6 papers
Classification of cohomogeneity-one actions on symmetric spaces of noncompact type
Ivan Solonenko, Víctor Sanmartín-López
We complete the classification of isometric cohomogeneity-one actions on all symmetric spaces of noncompact type up to orbit equivalence.
The spinor and Weierstrass representations of surfaces in space
Ivan Solonenko
In this paper, following Sullivan, Kusner, and Schmitt, we study conformal immersions of Riemann surfaces into the three-dimensional Euclidean space. Regarding such immersions as s…
Automorphisms of real semisimple Lie algebras and their restricted root systems
Ivan Solonenko
We prove that every automorphism of the restricted root system of a real semisimple Lie algebra -- when defined properly -- can be lifted to an automorphism of that Lie algebra. In…
Homogeneous codimension-one foliations on reducible symmetric spaces of noncompact type
Ivan Solonenko
We extend the classification of homogeneous codimension-one foliations on irreducible Riemannian symmetric spaces of noncompact type obtained by Berndt and Tamaru to the reducible…
Sections of polar actions
Juan Manuel Lorenzo-Naveiro, Ivan Solonenko
In this short note we provide an elementary proof of the folklore result in the theory of isometric Lie group actions on Riemannian manifolds asserting that sections of polar actio…
Classification of homogeneous hypersurfaces in some noncompact symmetric spaces of rank two
Ivan Solonenko
We classify, up to isometric congruence, the homogeneous hypersurfaces in the Riemannian symmetric spaces $\mathrm{SL}(3,\mathbb{H})/\mathrm{Sp}(3), \hspace{1pt} \mathrm{SO}(5,\mat…