The derivation-commutator
$R \cdot C - C \cdot R$ of a
semi-Riemannian manifold $(M,g)$, $\dim M \geq 4$, formed by its
Riemann-Christoffel curvature tensor
$R$ and the Weyl conformal curvature tensor $C$,
under some assumptions,
can be expressed
as a linear combination of $(0,6)$-Tachibana tensors $Q(A,T)$,
where $A$ is a symmetric $(0,2)$-tensor and $T$
a generalized curvature tensor. These conditions
form a family of generalized Einstein metric conditions.
In this survey paper we present recent results
on manifolds and submanifolds, and in particular hypersurfaces,
satisfying such conditions.
Warped product manifold Einstein quasi-Einstein 2-quasi-Einstein and partially Einstein manifold generalized Einstein metric condition pseudosymmetry type curvature condition hypersurface Chen ideal submanifold
Birincil Dil | İngilizce |
---|---|
Konular | Cebirsel ve Diferansiyel Geometri |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Erken Görünüm Tarihi | 15 Ekim 2023 |
Yayımlanma Tarihi | 29 Ekim 2023 |
Kabul Tarihi | 10 Eylül 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 16 Sayı: 2 |