Results 181 to 190 of about 95,729 (224)
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 ...
Wenjie Wang
semanticscholar +4 more sources
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 ...
Peter Bueken, L. Vanhecke
semanticscholar +4 more sources
Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds
Geometriae Dedicata, 2007 A pseudo-Riemannian manifold \((M,g)\) with the Ricci tensor \(\rho\) is called Ricci cyclic parallel if \[ (\nabla_X \rho)(Y,Z) + (\nabla_Y \rho)(Z,X) + (\nabla_Z \rho)(X,Y) =0,\quad X,Y,Z \in TM \] and it is called Ricci-Codazzi manifold if \[ (\nabla_X \rho)(Y,Z) = (\nabla_Y \rho)(X,Z), \quad X,Y,Z \in TM .
Giovanni Calvaruso
semanticscholar +4 more sources
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 ...
Jaeman Kim
openalex +2 more sources
Einstein-Like Curvature Homogeneous Lorentzian Three-Manifolds
Results in Mathematics, 2009 We completely classify three-dimensional curvature homogeneous Lorentzian manifolds equipped with either Einstein-like or conformally flat metrics. New examples arise, with respect to both locally homogeneous and curvature homogeneous up to order one examples [8, 9].
Giovanni Calvaruso
openalex +3 more sources
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.
Amirhesam Zaeim, Ali Haji‐Badali
openalex +3 more sources
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 ...
Fabio Podest�, Andrea Spiro
openalex +4 more sources
Einstein-like manifolds which are not Einstein
Geometriae Dedicata, 1978 Alfred Gray
openalex +3 more sources
Einstein-like and conformally flat contact metric three-manifolds.
, 2000 Let \((M,\eta, g,\xi, \phi)\) be a contact metric three-manifold. In this paper the author gives the following interesting classification results. a) The Ricci tensor of \(M\) is cyclic-parallel if and only if \(M\) is locally isometric to a naturally reductive homogeneous space.
Giovanni Calvaruso
openalex +4 more sources
EINSTEIN-LIKE METRICS ON FLAG MANIFOLDS
Modern Approaches to Differential Geometry and its Related FieldsAndreas Arvanitoyeorgos +2 more
openalex +2 more sources