On contact pseudo-metric manifolds satisfying a nullity condition

Ghaffarzadeh, Narges; Faghfouri, Morteza

doi:10.1016/j.jmaa.2020.124849

Cited by 2 publications

(7 citation statements)

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“…Studying nullity conditions on manifolds is one of the interesting topics in differential geometry, specially in the context of contact pseudo-metric manifolds. In [15], Ghaffarzadeh and second author introduced the notion of a (κ, µ)−contact pseudo-metric manifold. According to them a contact pseudometric manifold (M, ϕ, ξ, η) is called a (κ, µ)−contact pseudo-metric manifold if it satisfies…”

Section: η−Ricci Solitons On Sasakian Pseudo-metric Manifoldsmentioning

confidence: 99%

“…where R is the Riemannian curvature tensor of M , κ, µ are constant real numbers, and X, Y are arbitrary vector fields. For a (κ, µ) − contact pseudo-metric manifold we have the following formulas [15] h…”

Section: η−Ricci Solitons On Sasakian Pseudo-metric Manifoldsmentioning

confidence: 99%

“…Recently, Calvaruso and Perrone [8] have studied a contact pseudo-metric manifold in the general case. Ghaffarzadeh and second author studied nullity conditions on the contact pseudo-metric manifolds and have introduced the "(κ, µ)−contact pseudo-metric manifold" notion [15]. The relevance for the general relativity of contact pseudo-metric manifolds was studied in [12].…”

Section: Introductionmentioning

confidence: 99%

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$η-$Ricci solitons on contact pseudo-metric manifolds

Asgharzadeh,

Faghfouri

2021

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In this paper, we prove that a Sasakian pseudo-metric manifold which admits an η−Ricci soliton is an η−Einstein manifold, and if the potential vector field of the η−Ricci soliton is not a Killing vector field then the manifold is D−homothetically fixed, and the vector field leaves the structure tensor field invariant. Next, we prove that a K−contact pseudo-metric manifold with a gradient η−Ricci soliton metric is η−Einstein. Moreover, we study contact pseudo-metric manifolds admitting an η−Ricci soliton with a potential vector field point wise colinear with the Reeb vector field. Finally, we study gradient η−Ricci solitons on (κ, µ)-contact pseudo-metric manifolds.

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Section: η−Ricci Solitons On Sasakian Pseudo-metric Manifoldsmentioning

confidence: 99%

Section: η−Ricci Solitons On Sasakian Pseudo-metric Manifoldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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$η-$Ricci solitons on contact pseudo-metric manifolds

Asgharzadeh,

Faghfouri

2021

Preprint

Self Cite

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“…), we call (κ, µ)-contact pseudo-metric manifold, where (κ, µ) ∈ R 2 (see [4] for more details). Take now an arbitrary pseudo-metric manifold (M, g).…”

Section: The Contact Pseudo-metric Structure Of the Unit Tangent Sphe...mentioning

confidence: 99%

“…Takahashi [10] introduced contact pseudo-metric structures. Recently, contact pseudo-metric manifolds have been studied by Calvaruso and Perrone [2,6] and authors of this paper [4] introduce and study (κ, µ)-contact pseudometric manifolds.…”

Section: Introductionmentioning

confidence: 99%