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Einstein-like warped product manifolds

International Journal of Geometric Methods in Modern Physics, 2017
In this paper, it is proved that the fiber manifold [Formula: see text] of a warped product manifold [Formula: see text] inherits the Einstein-like class type of [Formula: see text] whereas the base manifold does under some conditions. Some related results are considered.
Mantica, Carlo Alberto, Shenawy, Sameh
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Three- and Four-Dimensional Einstein-like Manifolds and Homogeneity

Geometriae Dedicata, 1999
This paper is a contribution to the problem of classifying three- and four-dimensional Ricci-curvature homogeneous Einstein-like Riemannian manifolds. We recall that a Ricci-curvature homogeneous space is characterized by the constancy of the eigenvalues of the Ricci-operator and that \((M,g)\) is called Einstein-like if its Ricci-curvature tensor is ...
Lieven Vanhecke
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On a class of almost Kenmotsu manifolds admitting an Einstein like structure

São Paulo Journal of Mathematical Sciences, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dibakar Dey, Pradip Majhi
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Trans-Sasakian 3-manifolds with Einstein-like Ricci operators

Quaestiones Mathematicae, 2021
Let M be a trans-Sasakian 3-manifold such that the Ricci curvature of the structure vector field vanishes. In this paper, it is proved that if M is compact, then it is homothetic to a cosymplectic manifold. Without the compactness assumption, we prove that M is locally isometric to the product of R and a Kӓhler surface of constant curvature if the ...
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Generalized Einstein tensor for a Weyl manifold and its applications

Acta Mathematica Sinica, English Series, 2013
It is well known that the Einstein tensor G for a Riemannian manifold defined by R (alpha) (beta) = g (beta gamma) R (gamma I +/-) where R (gamma I +/-) and R are respectively the Ricci tensor and the scalar curvature of the manifold plays an important ...
Abdülkadir Özdeğer, Özdeğer, Abdülkadir   +1 more
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Remarks on Einstein-like Hermitian manifolds

Periodica Mathematica Hungarica, 2010
The main purpose of the paper under review is to study Hermitian manifolds \(M^{2n}=(M^{2n},J, g)\) of dimension \(2n\geq 4\). The author investigates for these manifolds some relations between such conditions as: an Einstein Hermitian manifold, a weakly \(\ast\)-Einstein Hermitian manifold, a \(c\)-Einstein Hermitian manifold, a \(J\)-invariant Ricci ...
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Einstein-like Pseudo-Riemannian Homogeneous Manifolds of Dimension Four

Mediterranean Journal of Mathematics, 2016
In this paper the authors classify four-dimensional homogeneous pseudo-Riemannian manifolds satisfying relaxed variants of the Einstein condition. More precisely: First, a pseudo-Riemannian manifold \((M,g)\) is \textit{Ricci-parallel} if its Ricci tensor is parallel with respect to its own Levi-Civita connection.
Zaeim, Amirhesam, Haji-Badali, Ali
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Four-dimensional Einstein-like manifolds and curvature homogeneity

Geometriae Dedicata, 1995
A Riemannian manifold \((M,g)\) is said to be curvature homogeneous if for any two points \(p, q \in M\), there exists a linear isometry \(F : T_p M \to T_q M\) such that \(F^* R = R_p\), where \(R\) denotes the Riemannian curvature tensor. In dimension two and three this is equivalent to the constancy of the eigenvalues of the Ricci operator \(Q ...
F. Podestà, SPIRO, Andrea
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