arXiv subjects
Publications and source records attributed to A. C. Bezerra.
We will present an estimate for the first eigenvalue of the Dirichlet and Neumann problems in terms of the Bakry-Émery Ricci curvature for a compact weighted manifold. As an application we will establish a stability condition for a h-minimal hypersurface.
In this paper we establish conditions on the length of the traceless part of the second fundamental form of a complete constant mean curvature hypersurface immersed in a space of constant sectional curvature in order to show that it is totally umbilical.
The purpose of this article is to study the geometry of gradient almost Yamabe solitons immersed into warped product manifolds $I\times_{f}M^{n}$ whose potential is given by the height function from the immersion. First, we present some geometric rigidity on compact solitons due to a curvature condition on the warped product manifold. In the sequel, we investigate conditions for the existence of totally geodesic, totally umbilical and minimal solitons. Furthermore, in the scope of constant angle immersions, a classification of rotational gradient almost Yamabe soliton immersed into $\mathbb{R}\times_{f}\mathbb{R}^{n}$ is also made.