Compact Einstein warped product manifolds

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• 作者：Abdoul Salam Diallo (1)
  
• 关键词：Einstein metric ; Warped product ; 53B05 ; 53B15 ; 53C50
• 刊名：Afrika Matematika
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：25
• 期：2
• 页码：267-270
• 全文大小：
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  4. Kim, D.-S.: Einstein warped product spaces. Honam. Math. J. 22, 107鈥?11 (2000)
  5. Kim, D.-S., Kim, Y.H.: Compact Einstein warped product spaces with nonpositive scalar curvature. Proc. Am. Math. Soc. 131, 2573鈥?576 (2003) CrossRef
  6. Kim, S.: Warped products and Einstein metrics. J. Phys. A Math. Gen. 39, L329鈥?33 (2006) CrossRef
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  8. O鈥橬eill, B.: Semi-Riemannian geometry with application to relativity. Academic Press, New York (1983)
  
• 作者单位：Abdoul Salam Diallo (1)
  
  1. African Institute for Mathematical Sciences, AIMS-S茅n茅gal, Km2 Route de Joal (Centre IRD de Mbour), B.P. 64 566, Dakar Fann, Senegal
  
• ISSN：2190-7668

文摘

The warped product \(B\times _f F\) of two Riemannian manifolds \((B,g_B)\) and \((F,g_F)\) with warping function \(f\) is the product manifold \(B\times F\) equipped with the warped product metric \(g_B + f^2 g_F\) , where \(f\) is a positive function on \(B\) . It is well-known that the notion of warped products plays some important roles in differential geometry as well as in general relativity. In this paper, we will survey recent results on the existence of compact Einstein warped product Riemannian manifolds.