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On Einstein sequential warped product spaces
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 3, pp. 379-394 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, Einstein sequential warped product spaces are studied. Here we prove that if $M$ is an Einstein sequential warped product space with negative scalar curvature, then the warping functions are constants. We find out some obstructions for the existence of such Einstein sequential warped product spaces. We also show that if $\bar{M}=(M_1\times_f I_{M_2})\times_{\bar{f}} I_{M_3}$ is a sequential warped product of a complete connected $(n-2)$-dimensional Riemannian manifold $M_1$ and one-dimensional Riemannian manifolds $I_{M_2}$ and $I_{M_3}$ with some certain conditions, then $(M_1, g_1)$ becomes a $(n-2)$-dimensional sphere of radius $\rho=\frac{n-2}{\sqrt{r^1+\alpha}}.$ Some examples of the Einstein sequential warped product space are given in Section 3. 
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Sampa Pahan; Buddhadev Pal. On Einstein sequential warped product spaces. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 3, pp. 379-394. http://geodesic.mathdoc.fr/item/JMAG_2019_15_3_a5/

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