On Convexity of Hypersurfaces in the Hyperbolic Space

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Dirichlet Polyhedra for Cyclic Groups in Complex Hyperbolic Space

We prove that the Dirichlet fundamental polyhedron for a cyclic group generated by a unipotent or hyperbolic element y acting on complex hyperbolic «-space centered at an arbitrary point w is bounded by the two hypersurfaces equidistant from the pairs w, yw and w,y~lw respectively. The proof relies on a convexity property of the distance to an isometric flow containing y.

Hoph Hypersurfaces of Sasakian Space Form with Parallel Ricci Operator Esmaiel Abedi, Mohammad Ilmakchi Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...

$L_k$-biharmonic spacelike hypersurfaces in Minkowski $4$-space $mathbb{E}_1^4$

Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b

We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k