Add to ORKGAbstract. The problem of determining the Bonnet hypersurfaces in Rn+1, for n> 1, is studied here. These hypersurfaces are by definition those that can be isometrically mapped to another hypersurface or to itself (as locus) by at least one nontrivial isometry preserving the mean curvature. The other hypersurface and/or (the locus of) itself is called Bonnet associate of the initial hypersurface. The orthogonal net which is called A-net is special and very important for our study and it is described on a hypersurface. It is proved that, non-minimal hypersur-face in Rn+1 with no umbilical points is a Bonnet hypersurface if and only if it has an A-net
Abstract. We classify minimal hypersurfaces in Rn × Sm, n,m ≥ 2, which are invariant by the canonica...
Whether the only minimal stable complete hypersurfaces in Rn+1; 3 n 7; are hyperplanes, is an open...
If the mean curvature function of a codimension-one foliation is close enough to 0, then there is a ...
We know that Bonnet surfaces are the surfaces which can admit at least one non-trivial isometry that...
The structure equations for a two-dimensional manifold are introduced and two results based on the C...
We study surfaces in the hyperbolic four-space admitting isometric deformations preserving the lengt...
Two non-congruent surfaces that are isometric and have the same mean curva-ture at corresponding poi...
surfaces, homogeneous spaces. We solve the Bonnet problem for surfaces in the homogeneous 3-manifold...
A generic surface in Euclidean 3-space is determined uniquely by its metric and curvature. Classific...
In this note we classify all Bonnet pairs on a simply connected domain. Our main intent was to apply...
We show that the evolution of isoparametric hypersurfaces of Riemannian manifolds by the mean curvat...
Neste trabalho, mostraremos que uma superfície é de Bonnet se, e somente se for uma Anet, apresentad...
We solve Blaschke’s problem for hypersurfaces of dimension n ≥ 3. Namely, we determine all pairs of ...
Abstract. In these notes we compute the geodesic curvature on a surface in isothermal coordinates an...
Let M be a smooth $(=C^∈fty)$, compact, connected hypersurface of Euclidean $(n+1)$-space $Rn+1$,$n≥...
Abstract. We classify minimal hypersurfaces in Rn × Sm, n,m ≥ 2, which are invariant by the canonica...
Whether the only minimal stable complete hypersurfaces in Rn+1; 3 n 7; are hyperplanes, is an open...
If the mean curvature function of a codimension-one foliation is close enough to 0, then there is a ...
We know that Bonnet surfaces are the surfaces which can admit at least one non-trivial isometry that...
The structure equations for a two-dimensional manifold are introduced and two results based on the C...
We study surfaces in the hyperbolic four-space admitting isometric deformations preserving the lengt...
Two non-congruent surfaces that are isometric and have the same mean curva-ture at corresponding poi...
surfaces, homogeneous spaces. We solve the Bonnet problem for surfaces in the homogeneous 3-manifold...
A generic surface in Euclidean 3-space is determined uniquely by its metric and curvature. Classific...
In this note we classify all Bonnet pairs on a simply connected domain. Our main intent was to apply...
We show that the evolution of isoparametric hypersurfaces of Riemannian manifolds by the mean curvat...
Neste trabalho, mostraremos que uma superfície é de Bonnet se, e somente se for uma Anet, apresentad...
We solve Blaschke’s problem for hypersurfaces of dimension n ≥ 3. Namely, we determine all pairs of ...
Abstract. In these notes we compute the geodesic curvature on a surface in isothermal coordinates an...
Let M be a smooth $(=C^∈fty)$, compact, connected hypersurface of Euclidean $(n+1)$-space $Rn+1$,$n≥...
Abstract. We classify minimal hypersurfaces in Rn × Sm, n,m ≥ 2, which are invariant by the canonica...
Whether the only minimal stable complete hypersurfaces in Rn+1; 3 n 7; are hyperplanes, is an open...
If the mean curvature function of a codimension-one foliation is close enough to 0, then there is a ...