Compact Einstein warped product manifolds
- Abdoul Salam Diallo
- … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
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.
- Beem, J.K., Ehrlich, P., Easley, K.: Global Lorentzian Geometry, 2nd edn. Marcel Dekker, Inc., New York (1996)
- Besse, A. L.: Einstein Manifolds. Springer, Berlin (1987).
- Bishop, R.L., O’Neil, B.: Manifolds of negative curvature. Trans. Am. Math. Soc. 303, 161–168 (1969)
- Kim, D.-S.: Einstein warped product spaces. Honam. Math. J. 22, 107–111 (2000)
- Kim, D.-S., Kim, Y.H.: Compact Einstein warped product spaces with nonpositive scalar curvature. Proc. Am. Math. Soc. 131, 2573–2576 (2003) CrossRef
- Kim, S.: Warped products and Einstein metrics. J. Phys. A Math. Gen. 39, L329–333 (2006) CrossRef
- Mustafa, M.T.: A non-existence result for compact Einstein warped products. J. Phys. A Math. Gen. 38, L791–L793 (2005) CrossRef
- O’Neill, B.: Semi-Riemannian geometry with application to relativity. Academic Press, New York (1983)
- Compact Einstein warped product manifolds
- Print ISSN
- Online ISSN
- Additional Links
- Einstein metric
- Warped product
- Author Affiliations
- 1. African Institute for Mathematical Sciences, AIMS-Sénégal, Km2 Route de Joal (Centre IRD de Mbour), B.P. 64 566, Dakar Fann, Senegal