Generalized quasi-Einstein manifolds with harmonic anti-self dual Weyl tensor

Leandro, Benedito

doi:10.1007/s00013-016-0896-0

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Cited by 12 publications

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“…One has that half conformally flat quasi-Einstein manifolds are locally conformally flat in the Riemannian setting [19,28]. We refer to [26] for the gradient Ricci soliton case and to [42] for related work.…”

Section: Introductionmentioning

confidence: 99%

Half conformally flat generalized quasi-Einstein manifolds of metric signature (2,2)

et al. 2018

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Section: Introductionmentioning

confidence: 99%

Half conformally flat generalized quasi-Einstein manifolds of metric signature (2,2)

et al. 2018

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show abstract

On critical point equation of compact manifolds with zero radial Weyl curvature

Baltazar

2018

Geom Dedicata

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Let C be the space of smooth metrics g on a given compact manifold M n (n ≥ 3) with constant scalar curvature and unitary volume. The goal of this paper is to study the critical point of the total scalar curvature functional restricted to the space C (we shall refer to this critical point as CPE metrics) under assumption that (M, g) has zero radial Weyl curvature.Among the results obtained, we emphasize that in 3-dimension we will be able to prove that a CPE metric with nonnegative sectional curvature must be isometric to a standard 3-sphere. We will also prove that a n-dimensional, 4 ≤ n ≤ 10, CPE metric satisfying a L n/2 -pinching condition will be isometric to a standard sphere. In addition, we shall conclude that such critical metrics are isometrics to a standard sphere under fourth-order vanishing condition on the Weyl tensor.

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2017

Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications

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Generalized quasi-Einstein manifolds with harmonic anti-self dual Weyl tensor

Cited by 12 publications

References 17 publications

Half conformally flat generalized quasi-Einstein manifolds of metric signature (2,2)

Half conformally flat generalized quasi-Einstein manifolds of metric signature (2,2)

On critical point equation of compact manifolds with zero radial Weyl curvature

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