Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2019, Volume 15, Number 3, Pages 379–394
DOI: https://doi.org/10.15407/mag15.03.379
(Mi jmag734)
 

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
Full-text PDF (409 kB) Citations (5)
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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.
Funding agency Grant number
University Grants Commission F.4-2/2006(BSR)/MA/18-19/0007
The first author is supported by UGC-DSKPDF of India No. F.4-2/2006(BSR)/MA/18-19/0007.
Received: 05.01.2018
Revised: 26.06.2018
Bibliographic databases:
Document Type: Article
MSC: 53C21, 53C25, 53C50.
Language: English
Citation: Sampa Pahan, Buddhadev Pal, “On Einstein sequential warped product spaces”, Zh. Mat. Fiz. Anal. Geom., 15:3 (2019), 379–394
Citation in format AMSBIB
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\by Sampa~Pahan, Buddhadev~Pal
\paper On Einstein sequential warped product spaces
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2019
\vol 15
\issue 3
\pages 379--394
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\crossref{https://doi.org/10.15407/mag15.03.379}
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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