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- W2324138090 abstract "Abstract The aim of this paper is to prove a sharp inequality for the area of a four dimensional compact Einstein manifold (Σ, g Σ ) embedded into a complete five dimensional manifold ( M 5 , g ) with positive scalar curvature R and nonnegative Ricci curvature. Under a suitable choice, we have $area(Sigma)^{frac{1}{2}}inf_{M}R leq 8sqrt{6}pi$ . Moreover, occurring equality we deduce that (Σ, g Σ ) is isometric to a standard sphere ( $mathbb{S}$ 4 , g can ) and in a neighbourhood of Σ, ( M 5 , g ) splits as ((-ϵ, ϵ) × $mathbb{S}$ 4 , dt 2 + g can ) and the Riemannian covering of ( M 5 , g ) is isometric to $Bbb{R}$ × $mathbb{S}$ 4 ." @default.
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- W2324138090 date "2015-01-23" @default.
- W2324138090 modified "2023-09-26" @default.
- W2324138090 title "Rigidity in dimension four of area-minimising Einstein manifolds" @default.
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- W2324138090 doi "https://doi.org/10.1017/s030500411500002x" @default.
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