Related papers: Curvature-adapted hypersurfaces of 2-type in non-f…

We give some classifications of biharmonic hypersurfaces with constant scalar curvature. These include biharmonic Einstein hypersurfaces in space forms, compact biharmonic hypersurfaces with constant scalar curvature in a sphere, and some…

We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space $\Hnn$ and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in $\Hnn$ is…

A hypersurface $M^{n-1}$ in a real space-form ${\bf R}^n$, $S^n$ or $H^n$ is isoparametric if it has constant principal curvatures. For ${\bf R}^n$ and $H^n$, the classification of isoparametric hypersurfaces is complete and relatively…

We classify the homogeneous and isoparametric hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$. In the classification, besides the hypersurfaces $\mathbb{S}^1(r)\times\mathbb{S}^2,\,r\in (0,1]$, it appears a family of hypersurfaces with…

In this paper we give a characterization of real hypersurfaces in noncompact complex two-plane Grassmannian $SU_{2,m}/S(U_2 U_m)$, $m \geq 2$ with Reeb vector field $\xi$ belonging to the maximal quaternionic subbundle $\mathcal Q$. Then it…

In this paper, we prove that any closed minimal hypersurface $M^4$ in the $5$-dimensional unit sphere $\mathbb{S}^5$ with constant scalar curvature and constant $3$-th mean curvature must be isoparametric. To be precise, $M^4$ is either an…

We give the classification of constant mean curvature rotational surfaces of elliptic, hyperbolic, and parabolic type in the four-dimensional pseudo-Euclidean space with neutral metric.

This paper explains the construction of all hypersurfaces with constant mean curvature -- cmc -- and exactly two principal curvatures on any space form endowed with a semi-riemannian metric. Here we will consider riemannian hypersurfaces as…

In this article we provide a general construction when $n\ge3$ for immersed in Euclidean $(n+1)$-space, complete, smooth, constant mean curvature hypersurfaces of finite topological type (in short CMC $n$-hypersurfaces). More precisely our…

We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.

We consider compact hypersurfaces in an $(n+1)$-dimensional either Riemannian or Lorentzian space $N^{n+1}$ endowed with a conformal Killing vector field. For such hypersurfaces, we establish an integral formula which, especially in the…

We consider complete spacelike hypersurfaces with constant mean curvature in the open region of de Sitter space known as the steady state space. We prove that if the hypersurface is bounded away from the infinity of the ambient space, then…

We classify the hypersurfaces of $\Sf^n\times \R$ and $\Hy^n\times \R$ with constant sectional curvature and dimension $n\geq 3$.

Let $ M^{n+1} $ ($ n \ge 2 $) be a simply-connected space form of sectional curvature $ -\kappa^2 $ for some $ \kappa \geq 0 $, and $ I $ an interval not containing $ [-\kappa,\kappa] $ in its interior. It is known that the domain of a…

In this paper, geometric characterizations of conformally flat and radially flat hypersurfaces in $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$ are given by means of their extrinsic geometry. Under suitable…

In this paper we complete the study started in [Pi2] of evolution by inverse mean curvature flow of star-shaped hypersurface in non-compact rank one symmetric spaces. We consider the evolution by inverse mean curvature flow of a closed,…

In this paper, we obtain a Cartan type identity for curvature-adapted isoparametric hypersurfaces in symmetric spaces of compact type or non-compact type. This identity is a generalization of Cartan-D'Atri's identity for…

We establish the following Hadamard--Stoker type theorem: Let $f:M^n\rightarrow\mathscr{H}^n\times\mathbb R$ be a complete connected hypersurface with positive definite second fundamental form, where $\mathscr H^n$ is a Hadamard manifold.…

We classify all homothetical surfaces with constant mean curvature $H$ in the hyperbolic space $\mathbb{H}^3$. Using the upper half-space model with standard coordinates $(x,y,z)$, these surfaces are defined by the relation $z =…

We consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its $(2,0)$-part is holomorphic. When the complex dimension of the ambient space is equal to…