Deformation and rigidity results for the 2<i>k</i>‐Ricci tensor and the 2<i>k</i>‐Gauss‐Bonnet curvature

Caúla, Tiago; Lima, Levi Lopes de; Santos, Newton Luis

doi:10.1002/mana.201200228

Cited by 4 publications

(2 citation statements)

References 29 publications

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“…See also [21] or example 2.8 in [14]. Restricting to the time slice t = 0, we obtain the anti-de Sitter Schwarzschild metric (5.4) g adS−Sch = (1 + ρ 2 − 2m ρ n k −2 ) −1 dρ 2 + ρ 2 dΘ 2 .…”

Section: Penrose Inequality For Graphs Over H N With a Horizon Type Bmentioning

confidence: 90%

The GBC mass for asymptotically hyperbolic manifolds

Wang²,

Wu³

2013

Comptes Rendus. Mathématique

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The paper consists of two parts. In the first part, by using the Gauss-Bonnet curvature, which is a natural generalization of the scalar curvature, we introduce a higher order mass, the Gauss-Bonnet-Chern mass m H k , for asymptotically hyperbolic manifolds and show that it is a geometric invariant. Moreover, we prove a positive mass theorem for this new mass for asymptotically hyperbolic graphs and establish a relationship between the corresponding Penrose type inequality for this mass and weighted Alexandrov-Fenchel inequalities in the hyperbolic space H n . In the second part, we establish these weighted Alexandrov-Fenchel inequalities in H n for any horospherical convex hypersurface Σ Σ

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Section: Penrose Inequality For Graphs Over H N With a Horizon Type Bmentioning

confidence: 90%

The GBC mass for asymptotically hyperbolic manifolds

Wang²,

Wu³

2013

Comptes Rendus. Mathématique

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“…We start by computing the linearizations of the generalized Ricci tensors and Lovelock scalars. These are due to [dLS10] at constant curvature metrics and [CdLS13] for slightly more general metrics.…”

Section: Graham-lee Existencementioning

confidence: 99%

Poincaré-Lovelock metrics on conformally compact manifolds

Albin

2020

Advances in Mathematics

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An important tool in the study of conformal geometry, and the AdS/CFT correspondence in physics, is the Fefferman-Graham expansion of conformally compact Einstein metrics. We show that conformally compact metrics satisfying a generalization of the Einstein equation, Poincaré-Lovelock metrics, also have Fefferman-Graham expansions. Moreover we show that conformal classes of metrics that are near that of the round metric on the n-sphere have fillings into the ball satisfying the Lovelock equation, extending the existence result of Graham-Lee for Einstein metrics.

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Gauss-Bonnet-Chern mass and Alexandrov-Fenchel inequality

Wang

et al. 2016

Front. Math. China

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Deformation and rigidity results for the 2k‐Ricci tensor and the 2k‐Gauss‐Bonnet curvature

Cited by 4 publications

References 29 publications

The GBC mass for asymptotically hyperbolic manifolds

The GBC mass for asymptotically hyperbolic manifolds

Poincaré-Lovelock metrics on conformally compact manifolds

Gauss-Bonnet-Chern mass and Alexandrov-Fenchel inequality

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