arXiv subjects
Publications and source records attributed to Marcelo Barboza.
In this paper, by slightly modifying Li-Yau's technique so that we can handle drifting Laplacians, we were able to find three different gradient estimates for the warping function, one for each sign of the Einstein constant of the fiber manifold. As an application, we exhibit a nonexistence theorem for gradient almost Ricci solitons possessing certain metric properties on the base of the warped product.
In this paper we utilize symmetries in order to exhibit exact solutions to Einstein's equation of a perfect fluid on a static manifold all of whose spatial factor belongs to the conformal class of a Riemannian space of constant curvature.
In this paper, we look for properties of gradient Yamabe solitons on top of warped product manifolds. Utilizing the maximum principle, we find lower bound estimates for both the potential function of the soliton and the scalar curvature of the warped product. By slightly modifying Li-Yau's technique so that we can handle drifting Laplacians, we were able to find three different gradient estimates for the warping function, one for each sign of the scalar curvature of the fiber manifold. As an application, we exhibit a nonexistence theorem for gradient Yamabe solitons possessing certain metric properties on the base of the warped product.
The purpose of this article is to study gradient Yamabe soliton on warped product manifolds. First, we prove triviality results in the case of noncompact base with limited warping function, and for compact base. In order to provide nontrivial examples, we consider the base conformal to a semi-Euclidean space, which is invariant under the action of a translation group, and then we characterize steady solitons. We use this method to give infinitely many explicit examples of complete steady gradient Yamabe solitons.