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- W2951936712 abstract "A Riemannian metric $wht{g}$ with Ricci curvature $wht{ri}$ is called nontrivial quasi-Einstein, in the sense of Case, Shu and Wei, if it satisfies $(-a/f)wht{nab} df+wht{ri}=lambda wht{g}$, for a smooth nonconstant function $f$ and constants $lambda$ and $a>0$. If $a$ is a positive integer, by a result of Kim and Kim, such a metric forms a base for certain warped Einstein metrics. On a manifold $M$ of real dimension at least six, let $(g,t)$ be a pair consisting of a Kahler metric $g$ which is locally Kahler irreducible, and a nonconstant Killing potential $t$. Suppose the metric $wht{g}=g/t^2$ is nontrivial bee on $Msetminust^{-1}(0)$, and the associated function $f$ is locally a function of $t$. Then $(g,t)$ is an pair, a notion defined by Derdzinski and Maschler. This implies that $M$ is biholomorphic to an open set in the total space of a $CP^1$ bundle whose base manifold admits a Kahler-Einstein metric. If $M$ is additionally compact, it is a total space of such a bundle or complex projective space. Also, the function $f$ is affine in $t^{-1}$ with nonzero constants. Conversely, in all even dimensions $ngeq 4$, there exist sk pairs $(g,t)$ and corresponding nonzero constants $K$ and $L$ for which $g/t^2$ is nontrivial quasi-Einstein with $f=Kt^{-1}+L$. Additionally, a result of Case, Shu and Wei on the Kahler reducibility of nontrivial Kahler bers is reproduced in dimension at least six in a more explicit form." @default.
- W2951936712 created "2019-06-27" @default.
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- W2951936712 date "2008-07-05" @default.
- W2951936712 modified "2023-09-27" @default.
- W2951936712 title "Conformally Kahler base metrics for Einstein warped products" @default.
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