Hubble Space Telescope observations of the gravitational lens PG 1115+080 in the infrared show the known zl = 0.310 lens galaxy and reveal the zs = 1.722 quasar host galaxy. The main lens galaxy G is… Expand

A map between Riemannian manifolds is called harmonic if the divergence of its differential vanishes. The problem of harmonic representatives of homotopy groups of the Euclidean spheres is quite… Expand

Dupin submanifolds in lie sphere geometry.- The mean curvatures on the tubular hypersurfaces in a space of constant curvature.- Deformation of surfaces preserving principal curvatures.- Lectures on… Expand