• ÖZ

In this paper, we give a neutral relation between metallic structure and almost quadratic metric ϕ-structure.Considering N as a metallic Riemannian manifold, we show that the warped product manifold R f N has an almostquadratic metric ϕ-structure. We define Kenmotsu quadratic metric manifolds, which include cosymplectic quadraticmanifolds when $\beta=0$. Then we give nice almost quadratic metric ϕ-structure examples. In the last section, weconstruct a quadratic ϕ-structure on the hypersurface $M^n$ of a locally metallic Riemannian manifold $M^{n+1}$

• ÖZ

We give necessary and sufficient conditions for warped product manifolds (M, g), of dimension ⩾ 4, with 1 -dimensional base, and in particular, for generalized Robertson–Walker spacetimes, to satisfy some generalized Einstein metric condition. Namely, the difference tensor R·C−C ·R, formed from the curvature tensor R and the Weyl conformal curvature tensor C , is expressed by the Tachibana tensor Q(S, R) formed from the Ricci tensor S and R. We also construct suitable examples of such manifolds. They are quasi-Einstein, i.e. at every point of M rank (S − α g) ⩽ 1, for some α ∈ R, or non-quasi-Einstein.

• ÖZ

In this study we consider surfaces in the Euclidean space $E^{2+d}$ satisfying the conditions $\overline{R}\centerdot$ h = $L_h$Q(g,h) and $\overline{R}\centerdot$ h = ${L_A}_H$$\hat{Q}(A_H,h)$.