We shall introduce the singular curvature function on cuspidal edges of surfaces, which is
related to the Gauss-Bonnet formula and which characterizes the shape of cuspidal edges …

Recently we discovered a new geometry on submanifolds in hyperbolic n-space which is
called horospherical geometry. Unfortunately this geometry is not invariant under the …

Using the Legendrian dualities between surfaces in pseudo-spheres in Lorentz-Minkowski 4-
space, we study various kind of flat surfaces in pseudo-spheres. We consider a surface in …

Our first objective in this paper is to give a natural formulation of the Christoffel problem for
hypersurfaces in Hn+ 1, by means of the hyperbolic Gauss map and the notion of hyperbolic …

A mandala of Legendrian dualities for pseudo-spheres in semi-Euclidean space Page 1 A
mandala of Legendrian dualities for pseudo-spheres in semi-Euclidean space By Liang …

THE HOROSPHERICAL GEOMETRY OF SUBMANIFOLDS IN HYPERBOLIC SPACE Page
1 J. London Math. Soc. (2) 71 (2005) 779–800 Cо2005 London Mathematical Society doi:10.1112/S0024610705006447 …

We present surfaces with prescribed normal Gaussmap. These surfaces are obtained as the
envelope of a sphere congruencewhere the other envelope is contained in a plane. We …

We give a complete description of the flat surfaces in hyperbolic 3-space that are regularly
embedded around an isolated singularity. Specifically, we show that there is a one-to-one …

We give a construction that connects the Cauchy problem for the 2-dimensional elliptic
Liouville equation with a certain initial value problem for mean curvature one surfaces in …

We define discrete flat surfaces in hyperbolic $3 $-space $\mathbb {H}^ 3$ from the
perspective of discrete integrable systems and prove properties that justify the definition. We …