arXiv subjects

Johnatan Costa

Publications and source records attributed to Johnatan Costa.

3 recordsLinked to original sources

arXiv2025

On quasi-Einstein manifolds with constant scalar curvature

In this article, we study quasi-Einstein manifolds with constant scalar curvature. We provide a classification of compact and noncompact (possibly with boundary) $T$-flat quasi-Einstein manifolds with constant scalar curvature, where the $T$-tensor is directly related to the Cotton and Weyl tensors. Moreover, we construct new explicit examples of noncompact quasi-Einstein manifolds. In addition, we prove a complete classification of compact and noncompact (possibly with boundary) $3$-dimensional $m$-quasi-Einstein manifolds with constant scalar curvature.

math.DG↗

arXiv2024

Rigidity of compact quasi-Einstein manifolds with boundary

In this article, we investigate the geometry of compact quasi-Einstein manifolds with boundary. We show that a $3$-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature is isometric, up to scaling, to either the standard hemisphere $\mathbb{S}^{3}_{+}$, or the cylinder $I\times\mathbb{S}^2$ with the product metric. For dimension $n=4,$ we prove that a $4$-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature is isometric, up to scaling, to either the standard hemisphere $\mathbb{S}^{4}_{+},$ or the cylinder $I\times\mathbb{S}^3$ with the product metric, or the product space $\mathbb{S}^{2}_{+}\times\mathbb{S}^2$ with the product metric. Other related results for arbitrary dimensions are also discussed.

math.DG↗

arXiv2023

Geometry of static perfect fluid space-time

In this article, we investigate the geometry of static perfect fluid space-time on compact manifolds with boundary. We use the generalized Reilly's formula to establish a geometric inequality for a static perfect fluid space-time involving the area of the boundary and its volume. Moreover, we obtain new boundary estimates for static perfect fluid space-time. One of the boundary estimates is obtained in terms of the Brown-York mass and another one related to the first eigenvalue of the Jacobi operator. In addition, we provide a new (simply connected) counterexample to the Cosmic no-hair conjecture for arbitrary dimension $n\geq 4.$

math.DG↗