We classify real hypersurfaces in a nonflat complex space form of complex dimension two
which are weakly or strongly Einstein. Specifically, first we prove that a Hopf hypersurface of …

Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds - ScienceDirect
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A Riemannian manifold $(M, g) $ is called\emph {weakly Einstein} if the tensor $ R_ {iabc}
R_ {j}^{~~ abc} $ is a scalar multiple of the metric tensor $ g_ {ij} $. We give a complete …

It is shown that locally conformally flat weakly-Einstein manifolds are either locally
symmetric, and hence a product N_1^ m (c) * N_2^ m (-c) N 1 m (c)× N 2 m (-c), or otherwise …

Let ğMn, gŞ be an n-dimensional Riemannian manifold. Let 'be the Levi-Civita connection
and let R be the curvature operator chosen with the sign convention RğX, Y޼½ 'X,'Y Š À …

The goal of this paper is to study weakly Einstein critical metrics of the volume functional on
a compact manifold M with smooth boundary∂ M. Here, we will give the complete …

In this paper, we prove that a real hypersurface in CP 2 (c) and CH 2 (c) is strongly Einstein if
and only if it is locally congruent to a geodesic sphere with radius d= 2 ln (2+ 1)/-c in CH 2 …

Index formulas for the curvature tensors of an invariant metric on a Lie group are obtained.
The results are applied to the case of solvable Lie algebras that have a codimension one …

Riemannian four-manifolds in which the triple contraction of the curvature tensor against
itself yields a functional multiple of the metric are called weakly Einstein. We focus on weakly …

A Riemannian manifold is called\emph {weakly Einstein} if the tensor $ R_ {iabc} R_ {j}^{~~
abc} $ is a scalar multiple of the metric tensor $ g_ {ij} $. We consider weakly Einstein Lie …