Gap results for compact quasi-Einstein metrics

Linfeng, Wang

doi:10.1007/s11425-016-9049-9

Cited by 8 publications

(5 citation statements)

References 20 publications

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“…By the compactness of manifold M , there exists some global minimum point q ∈ M of the potential function f . Due to (2.25), the maximum principle shows that ̺e 2 τ f (q) ≤ τ λ, which gives 1 (τ − mδ)λ ̺e Then, it follows from the above that arctan 1 (τ − mδ)λ ̺e We deduce from (5.16) that (see [29]) Hence, we arrive at (5.11). Now, we prove (5.12).…”

Section: 1mentioning

confidence: 77%

“…3), then the τ -quasi Ricci-harmonic metric is exactly a τ -quasi Einstein metric, see [5,11,29]. We know from [2] that τ -quasi Einstein metrics are closely relative to the existence of warped product Einstein manifolds for any positive integer τ .…”

Section: Introductionmentioning

confidence: 99%

“…In the third part of this paper, we shall extend gap theorems for compact gradient Ricci solitons [9], for compact Ricci-harmonic solitons [22] and for compact τ -quasi-Einstein metrics [29] to the case of compact τ -quasi Ricciharmonic metrics.…”

Section: Introductionmentioning

confidence: 99%

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Rigidity of τ-quasi Ricci-harmonic metrics

Zeng

2018

Indian J Pure Appl Math

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In this paper, we study compact generalized τ -quasi Ricciharmonic metrics. In the first part, we explore conditions under which generalized τ -quasi Ricci-harmonic metrics are harmonic-Einstein and give some characterization results for it. In the second part, we obtain some rigidity results for compact (τ, ρ)-quasi Ricci-harmonic metrics which are special case of generalized τ -quasi Ricci-harmonic metrics. In the third part, we shall give two gap theorems for compact τ -quasi Ricci-harmonic metrics by showing some necessary and sufficient conditions for the metrics to be harmonic-Einstein.where ∇φ ⊗ ∇φ := φ * h is the pull-back of the metric h via φ and τ g φ = trace∇dφ denotes the tension field of φ with respect to g [8], and Ric f,τ 2010 Mathematics Subject Classification. Primary 53C21, Secondary 53C25.

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Section: 1mentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

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Rigidity of τ-quasi Ricci-harmonic metrics

Zeng

2018

Indian J Pure Appl Math

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“…For a general manifold, quasi-Einstein metrics have been studied in depth and some rigid properties and gap results were obtained (cf. [9,20,21]). Later on Barros-Ribeiro Jr [4] and Limoncu [16] generalized and studied the previous equation (1.1), independently, by considering a 1-form V ♭ instead of df , which is satisfied Ric + 1 2…”

Section: Introductionmentioning

confidence: 99%

Quasi-Einstein structures and almost cosymplectic manifolds

Chen

2020

RACSAM

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In this article, we study almost cosymplectic manifolds admitting quasi-Einstein structures (g, V, m, λ). First we prove that an almost cosymplectic (κ, µ)-manifold is locally isomorphic to a Lie group if (g, V, m, λ) is closed and on a compact almost (κ, µ)-cosymplectic manifold there do not exist quasi-Einstein structures (g, V, m, λ), in which the potential vector field V is collinear with the Reeb vector filed ξ. Next we consider an almost α-cosymplectic manifold admitting a quasi-Einstein structure and obtain some results. Finally, for a K-cosymplectic manifold with a closed, non-steady quasi-Einstein structure, we prove that it is η-Einstein. If (g, V, m, λ) is non-steady and V is a conformal vector field, we obtain the same conclusion.

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“…For a general manifold, quasi-Einstein metrics have been studied in depth and some rigid properties and gap results were obtained (cf. [2,17,18]). On the other hand, we also notice that for the odd-dimensional manifold, Ghosh in [8] studied quasi-Einstein contact metric manifolds.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Einstein hypersurfaces of complex space forms

Chen¹

2019

Preprint

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Based on a well-known fact that there are no Einstein hypersurfaces in a non-flat complex space form, in this article we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hyersurface of a non-flat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of [5].

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Gap results for compact quasi-Einstein metrics

Cited by 8 publications

References 20 publications

Rigidity of τ-quasi Ricci-harmonic metrics

Rigidity of τ-quasi Ricci-harmonic metrics

Quasi-Einstein structures and almost cosymplectic manifolds

Quasi-Einstein hypersurfaces of complex space forms

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