In this survey article we introduce the notion of frontals, which provides a class of
generalised submanifolds with singularities but with well-defined tangent spaces. We …

We study geometric properties of caustics of pseudo-spherical surfaces, that is, surfaces with
constant negative Gaussian curvature-1 in the Euclidean 3-space ℝ 3. We investigate the …

We study locally harmonic maps between a Riemann surface or Lorentz surface $ M $ and a
Riemann surface or Lorentz surface $ N $. All four cases are studied in a unified way …

DEFORMATIONS OF CUSPIDAL EDGES IN A 3-DIMENSIONAL SPACE FORM Kentaro Saji,
Masaaki Umehara and Kotaro Yamada Abstract Introducti Page 1 K. SAJI, M. UMEHARA AND …

We study the surfaces of constant positive Gauss curvature in Euclidean 3-space via the
harmonicity of the Gauss map. Using the loop group representation, we solve the regular …

We study locally harmonic maps between a Riemann surface or a Lorentz surface M and a
Riemann or Lorentz surface N. All four cases are written using a unified formalism. Therefore …

Wave maps (or Lorentzian-harmonic maps) from a $1+ 1$-dimensional Lorentz space into
the $2 $-sphere are associated to constant negative Gaussian curvature surfaces in …

Архитекторы, работающие с оболочками, используют в своих проектах, в основном,
хорошо зарекомендовавшие себя геометрические формы, которые составляют …

Architects, designing shells, use in their projects, as a rule, geometrical forms well proved
themselves, that constitute 5-10% from the surfaces known to geometricians. But there is …

On the minimality condition for caustics of pseudo-spherical surfaces Page 1 PROCEEDINGS
OF THE AMERICAN MATHEMATICAL SOCIETY Volume 152, Number 7, July 2024, Pages …