arXiv subjects

Marcelo Bezerra Barboza

Publications and source records attributed to Marcelo Bezerra Barboza.

2 recordsLinked to original sources

arXiv2023

Classification of gradient Yamabe soliton hypersurfaces of space forms

In this paper we investigate gradient Yamabe solitons, either steady or shrinking, that can be isometrically immersed into space forms as hypersurfaces that admit an upper bound on the norm of their second fundamental form. Those solitons satisfying an additional condition, that could be constant mean curvature or the number of critical points of the potential function being at most one, are fully classified. Our argument is based on the weak Omori-Yau principle for the drifted Laplacian on Riemannian manifolds.

math.DG↗

arXiv2020

Rigidity results for quotient almost Yamabe solitons

In this paper we investigate the structure of certain solutions of the fully nonlinear Yamabe flow, which we call quotient almost Yamabe solitons because they extend quite naturally those called quotient Yamabe solitons. We then present sufficient conditions for a compact quotient almost Yamabe soliton to be either trivial or isometric with an Euclidean sphere. We also characterize noncompact quotient gradient almost Yamabe solitons satisfying certain conditions on both its Ricci tensor and potential function.

math.DG↗