Related papers: Closed Biconservative Hypersurfaces in Spheres

Biconservative surfaces of Riemannian 3-space forms $N^3(\rho)$, are either constant mean curvature (CMC) surfaces or rotational linear Weingarten surfaces verifying the relation $3\kappa_1+\kappa_2=0$ between their principal curvatures…

For every $p\in\mathbb{R}$, we study $p$-elastic curves in the hyperbolic plane $\mathbb{H}^2$ and in the de Sitter $2$-space $\mathbb{H}_1^2$. We analyze the existence of closed $p$-elastic curves with nonconstant curvature showing that in…

Biconservative hypersurfaces are hypersurfaces which have conservative stress-energy tensor with respect to the bienergy, containing all minimal and constant mean curvature hypersurfaces. The purpose of this paper is to study biconservative…

For $p\in\mathbb{R}$, we show that non-circular closed $p$-elastic curves in $\mathbb{S}^2$ exist only when $p=2$, in which case they are classical elastic curves, or when $p\in(0,1)$. In the latter case, we prove that for every pair of…

We classify non-minimal biconservative surfaces with parallel mean curvature vector field in $\mathbb{S}^n\times\mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$. When these surfaces do not lie in $\mathbb{S}^n$ or $\mathbb{H}^n$ and they are…

In this article we study $p$-biharmonic curves as a natural generalization of biharmonic curves. In contrast to biharmonic curves $p$-biharmonic curves do not need to have constant geodesic curvature if $p=\frac{1}{2}$ in which case their…

In this paper we present alternative proofs for two known rigidity results concerning non-negatively curved compact biconservative hypersurfaces in space forms. Further, we prove some new rigidity results by replacing the hypothesis of…

We survey some recent results on biconservative surfaces in $3$-dimensional space forms $N^3(c)$ with a special emphasis on the $c=0$ and $c=1$ cases. We study the local and global properties of such surfaces, from extrinsic and intrinsic…

Let m>1 and n>1 be any pair of integers. In this paper we prove that if H is between the numbers \cot(\frac{\pi}{m}) and b_{m,n}=\frac{(m^2-2)\sqrt{n-1}}{n\sqrt{m^2-1}}, then, there exists a non isoparametric, compact embedded hypersurface…

We construct simply connected, complete, non-$CMC$ biconservative surfaces in the $3$-dimensional hyperbolic space $\mathbb{H}^3$ in an intrinsic and extrinsic way. We obtain three families of such surfaces, and, for each surface, the set…

In this paper, we describe a family of embedded hypersurfaces with constant mean curvature (CMC) in the $(n+1)$-dimensional unit sphere. In the process, we provide evidence for new CMC embedded examples. In particular, for some examples…

In this paper, we study biconservative hypersurfaces of index 2 in $\mathbb E^{5}_{2}$. We give the complete classification of biconservative hypersurfaces with diagonalizable shape operator at exactly three distinct principal curvatures.…

Biconservative hypersurfaces are hypersurfaces with conservative stress-energy tensor with respect to the bienergy functional, and form a geometrically interesting family which includes that of biharmonic hypersurfaces. In this paper we…

Biconservative submanifolds arise as a natural relaxation of the biharmonic condition and play an important role in the submanifold theory. In this paper, we study non-CMC biconservative surfaces with parallel normalized mean curvature…

We approach the one-parameter family of rotational constant mean curvature (CMC) spheres of $\mathbb H^n\times\mathbb R$ and $\mathbb S^n\times\mathbb R$ focusing on their stability and isoperimetry properties. We prove that all rotational…

We prove that in Euclidean space $R^{n+1}$ any compact immersed nonnegatively curved hypersurface $M$ with free boundary on the sphere $S^n$ is an embedded convex topological disk. In particular, when the $m^{th}$ mean curvature of $M$ is…

We study hypersurfaces in the pseudo-Euclidean space $\mathbb{E}^{n+1}_s$, which write as a warped product of a $1$-dimensional base with an $(n-1)$-manifold of constant sectional curvature. We show that either they have constant sectional…

In this paper, we study biconservative surfaces with parallel normalized mean curvature vector field ($PNMC$) in the $4$-dimensional unit Euclidean sphere $\mathbb{S}^4$. First, we study the existence and uniqueness of such surfaces. We…

In this paper, we extend our investigation of the class of biconservative surfaces with non-constant mean curvature in 4-dimensional space forms $N^4(\epsilon)$. Specifically, we focus on biconservative surfaces with non-parallel normalized…

In this article we consider PMC surfaces in complex space forms, and we study the interaction between the notions of PMC, totally real and biconservative. We first consider PMC surfaces in non-flat complex space forms and we prove that they…