Para-Sasaki-like Riemannian manifolds and new Einstein metrics

Ivanov, Stefan; Manev, Hristo; Manev, Mancho

doi:10.1007/s13398-021-01053-z

Cited by 11 publications

(15 citation statements)

References 7 publications

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“…Para-Sasaki-like manifolds. In [15], the class of para-Sasaki-like spaces is defined in the set of almost paracontact almost paracomplex Riemannian manifolds obtained from a specific cone construction. The considered para-Sasaki-like spaces are determined by…”

Section: Almost Paracontact Almost Paracomplex Riemannian Manifoldsmentioning

confidence: 99%

Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds

Manev

Tavkova

2019

J. Geom.

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Section: Almost Paracontact Almost Paracomplex Riemannian Manifoldsmentioning

confidence: 99%

Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds

Manev

Tavkova

2019

J. Geom.

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“…On the other hand, if we substitute z = v in the equality for R(ξ, y)z in (1), we get the following expression (10) R(ξ, y)v = −df (y)ξ + df (ξ)y.…”

Section: Proof Of the Main Resultsmentioning

confidence: 99%

“…In [10], a subclass called para-Sasaki-like Riemannian Π-manifolds of the considered manifolds is introduced and studied. It is determined as follows…”

Section: Preliminariesmentioning

confidence: 99%

Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $Π$-manifolds

Manev¹

2022

Preprint

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Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian Π-manifolds are studied. It is proved that these objects have constant soliton coefficients. For the soliton under study is shown that the corresponding scalar curvatures of the considered both metrics are equal and constant and its Ricci tensor is a constant multiple of the vertical component. Explicit example of a 3-dimensional para-Sasaki-like Riemannian Π-manifold is provided in support of the proved assertions.

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“…In [12], the class of para-Sasaki-like Riemannian Π-manifolds is introduced and studied. This special subclass of the considered manifolds is determined by:…”

Section: Para-sasaki-like Riemannian π-Manifoldsmentioning

confidence: 99%

“…On an arbitrary Riemannian Π-Manifolds (M, φ, ξ, η, g), there exists a symmetric (0, 2)-tensor ρ * (y, z) = g ij R(e i , y, z, φe j ) associated with ρ regarding φ. In the case of para-Sasaki-like (M, φ, ξ, η, g), the following property is valid [12]:…”

Section: Para-sasaki-like Riemannian π-Manifoldsmentioning

confidence: 99%

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $Π$-manifolds

Manev¹,

Manev²

2022

Preprint

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Para-Ricci-like solitons with arbitrary potential on para-Sasakilike Riemannian Π-manifolds are introduced and studied. For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of both metrics. Thus, the corresponding scalar curvatures of both considered metrics are equal and constant. An explicit example of the Lie group as the manifold under study is presented.

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Para-Sasaki-like Riemannian manifolds and new Einstein metrics

Cited by 11 publications

References 7 publications

Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds

Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds

Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $Π$-manifolds

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $Π$-manifolds

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