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This article is cited in 5 scientific papers (total in 5 papers)
On Einstein sequential warped product spaces
Sampa Pahana, Buddhadev Palb a Department of Mathematics, University of Kalyani, Nadia-741235, India
b Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India
Abstract:
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.
Key words and phrases:
warped product, sequential warped product, Einstein manifold.
Received: 05.01.2018 Revised: 26.06.2018
Citation:
Sampa Pahan, Buddhadev Pal, “On Einstein sequential warped product spaces”, Zh. Mat. Fiz. Anal. Geom., 15:3 (2019), 379–394
Linking options:
https://www.mathnet.ru/eng/jmag734 https://www.mathnet.ru/eng/jmag/v15/i3/p379
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Abstract page: | 106 | Full-text PDF : | 105 | References: | 12 |
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