Related papers: Compact Biconservative Hypersurfaces in Space Form…
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…
In this paper, we investigate the geometry of compact spacelike biconservative hypersurfaces with constant scalar curvature in de Sitter space $\mathbb{S}_1^{m+1}(c)$, under some geometric constraints. Our results extend the understanding…
We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of biconservative surfaces in 3-dimensional space forms.
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…
We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic…
In this paper we study biconservative hypersurfaces $M$ in space forms $\overline M^{n+1}(c)$ with four distinct principal curvatures whose second fundamental form has constant norm. We prove that every such hypersurface has constant mean…
In this paper we show that a particular extrinsic pointwise hypersurface invariant is always non-positive on minimal hypersurfaces of constant curvature spaces and vanishes identically if and only if the hypersurface is rotational. We show…
Biconservative surfaces are surfaces with divergence-free stress-bienergy tensor. Simply connected, complete, non-$CMC$ biconservative surfaces in $3$-dimensional space forms were constructed working in extrinsic and intrinsic ways. Then,…
We study in a uniform manner the properties of biconservative surfaces in arbitrary Riemannian manifolds. Biconservative surfaces being characterized by the vanishing of the divergence of a symmetric tensor field $S_2$ of type $(1,1)$,…
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…
In this article, under mild constraints on the sectional curvature, we exploit a divergence formula for symmetric endomorphisms to deduce a general Poincar\'e type inequality. We apply such inequality to higher-order mean curvature of…
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 show that the combination of non-negative sectional curvature (or $2$-intermediate Ricci curvature) and strict positivity of scalar curvature forces rigidity of complete (non-compact) two-sided stable minimal hypersurfaces in a…
In this paper, we give some new characterizations of umbilic hypersurfaces in general warped product manifolds, which can be viewed as generalizations of the work in \cite{KLP18} and \cite{WX14}. Firstly, we prove the rigidity for…
In this paper, we study Lorentzian biconservative hypersurfaces for which the gradient of their mean curvature $H$ is lightlike, i.e. $\langle \gr H,\gr H\rangle=0$. We establish the non-existence of such hypersurfaces in the Minkowski…
In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as "weighted'' mean curvatures, which extend the work…
We prove that compact non-flat manifolds with constant sectional curvature admit no conformal product structure. Furthermore, we demonstrate that the methods extend naturally to irreducible, compact locally symmetric spaces of non-positive…
In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also…
We present some general properties of biharmonic and biconservative submanifolds and then survey recent results on such hypersurfaces in space forms. We also propose an alternative version for a well-known result of Nomizu and Smyth for…
We introduce new biholomorphic invariants for real-analytic hypersurfaces in 2-dimensional complex space and show how they can be used to show that a hypersurface possesses few automorphisms. We give conditions, in terms of the new…