Timeline for Which Kahler Manifolds are also Einstein Manifolds?

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when toggle format	what		by	license	comment
Oct 23, 2017 at 21:48	comment	added	user21574		Let $M$ is a Kähler manifold of dimension $2n$, then $M$ is Kähler-Einstein if and only if $\tau(L)=\tau(L^⊥)$ for all n-plane sections $L⊂T_pM$, where $\tau$ is the scalar curvature, Chen, Bang-Yen, Dillen, Franki Totally real bisectional curvature, Bochner-Kaehler and Einstein-Kaehler manifolds. Differential Geom. Appl. 10 (1999), no. 2, 145–154.
May 22, 2013 at 5:56	history	edited	Michael Albanese		edited tags
Jan 27, 2012 at 6:21	answer	added	314159.		timeline score: 11
Sep 15, 2011 at 14:19	vote	accept	Dyke Acland
Mar 7, 2011 at 15:39	history	edited	Spiro Karigiannis		edited tags
Mar 7, 2011 at 14:11	answer	added	Dmitri Panov		timeline score: 41
Mar 7, 2011 at 14:07	comment	added	Henri		A theorem of Aubin-Yau says that any compact Kähler manifold with $c_1(X)$ negative or zero (as cohomology class) is Kähler-Einstein, in the sense that there exists $\omega$ a Kähler metric satisfyinf respectively $Ric(\omega)=-\omega$ (resp. $Ric(\omega)=0$). In the case where $c_1(X)>0$, it is not always true, but we know some examples (well-chosen weigted spaces e.g).
Mar 7, 2011 at 13:53	history	asked	Dyke Acland	CC BY-SA 2.5