Static perfect fluid space-time on compact manifolds

Coutinho, Fernando; Diógenes, R.; Leandro, Benedito; Ribeiro, E.

doi:10.1088/1361-6382/ab5402

Cited by 16 publications

(26 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The equality occurs if and only if M 3 is isometric to a standard hemisphere. Inspired by this result and its natural extension for static perfect fluid space-time with boundary ∂M [6] and generalized (λ, n + m)-Einstein manifolds [7], we obtain the next result for Einstein-type manifold.…”

Section: Introductionmentioning

confidence: 71%

“…To prove Theorem 1, we need the following Proposition from [6], which is a consequence of Obata's work [12] and Reilly's theorem [13].…”

Section: Background and Proofsmentioning

confidence: 99%

“…Barros and Gomes [2] proved that a compact gradient generalized m-quasi-Einstein metric with constant scalar curvature must be isometric to a standard Euclidean sphere S n with the potential f well determined. Later, Coutinho et al [6] studied the geometry of static perfect fluid space-time metrics on compact manifolds with boundary yielding a gap result for this space. Then, Freitas and Santos [7] investigated about generalized compact Einstein manifolds, giving some topological classifications for its boundary.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by [6] and [10], we obtain some characterization results for the Einstein-type manifolds with dimension n ≥ 3, compact and with boundary. Our first result is the following: Theorem 1.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Some characterizations of compact Einstein-type manifolds

Andrade¹,

Melo²

2022

Preprint

View full text Add to dashboard Cite

In this work, we investigate the geometry and topology of compact Einstein-type manifolds with nonempty boundary. First, we prove a sharp boundary estimate, as consequence we obtain under certain hypotheses that the Hawking mass is bounded from bellow in terms of area. Then we give a topological classification for its boundary. Finally, we prove a gap result for a compact Einstein-type manifold with boundary.

show abstract

Section: Introductionmentioning

confidence: 71%

“…To prove Theorem 1, we need the following Proposition from [6], which is a consequence of Obata's work [12] and Reilly's theorem [13].…”

Section: Background and Proofsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some characterizations of compact Einstein-type manifolds

Andrade¹,

Melo²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Additionally, on a Riemannian manifold (M, g), the static perfect fluid equation is (cf. [13][14][15])…”

Section: Introductionmentioning

confidence: 99%

On Minimal Hypersurfaces of a Unit Sphere

et al. 2021

View full text Add to dashboard Cite

Minimal compact hypersurface in the unit sphere Sn+1 having squared length of shape operator A2<n are totally geodesic and with A2=n are Clifford hypersurfaces. Therefore, classifying totally geodesic hypersurfaces and Clifford hypersurfaces has importance in geometry of compact minimal hypersurfaces in Sn+1. One finds a naturally induced vector field w called the associated vector field and a smooth function ρ called support function on the hypersurface M of Sn+1. It is shown that a necessary and sufficient condition for a minimal compact hypersurface M in S5 to be totally geodesic is that the support function ρ is a non-trivial solution of static perfect fluid equation. Additionally, this result holds for minimal compact hypersurfaces in Sn+1, (n>2), provided the scalar curvature τ is a constant on integral curves of w. Yet other classification of totally geodesic hypersurfaces among minimal compact hypersurfaces in Sn+1 is obtained using the associated vector field w an eigenvector of rough Laplace operator. Finally, a characterization of Clifford hypersurfaces is found using an upper bound on the integral of Ricci curvature in the direction of the vector field Aw.

show abstract

Compact quasi‐Einstein manifolds with boundary

Diógenes

Gadelha

2022

Mathematische Nachrichten

View full text Add to dashboard Cite

The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds similar to previous results obtained for static and 𝑉-static spaces. In addition, we show that compact quasi-Einstein manifolds with connected boundary and satisfying a suitable pinching condition must be isometric, up to scaling, to the standard hemisphere 𝕊 𝑛 + .

show abstract

Static perfect fluid space-time on compact manifolds

Cited by 16 publications

References 24 publications

Some characterizations of compact Einstein-type manifolds

Some characterizations of compact Einstein-type manifolds

On Minimal Hypersurfaces of a Unit Sphere

Compact quasi‐Einstein manifolds with boundary

Contact Info

Product

Resources

About