Timeline for Which Kahler Manifolds are also Einstein Manifolds?
Current License: CC BY-SA 2.5
7 events
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| Oct 23, 2017 at 19:43 | comment | added | user21574 | Smyth showed that a complete complex hypersurface of $\mathbb CP^{n+1}$ is an Kahler-Einstein with respect to the Kaehler metric induced from $CP^{n+1}$ if and only if it is either a complex hyperplane $\mathbb CP^n$ or an n-dimensional complex quadric. see Smyth, B., 'Differential Geometry of Complex Hypersurfaces', Ann. Math. 85 (1967), 246- 266. Compare with result of S.T.Yau | |
| Oct 23, 2017 at 19:41 | comment | added | user21574 | Let $M$ is an algebraic hypersurface of degree $d$ imbedded in $CP^{n+1}$ with the Kaehler metric induced from $CP^{n+1}$, then, by a theorem of Riemann-Roch-Hirzebruch, the first Chern class of $M$ is given by $c_1(M) = ((n + 2 - d)/4\pi)[\omega]$, BUT this never say that they are Kahler-Einstein! | |
| Sep 15, 2011 at 14:19 | vote | accept | Dyke Acland | ||
| Mar 9, 2011 at 22:54 | history | edited | Dmitri Panov | CC BY-SA 2.5 |
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| Mar 7, 2011 at 21:08 | history | edited | Charles Staats | CC BY-SA 2.5 |
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| Mar 7, 2011 at 14:22 | history | edited | Dmitri Panov | CC BY-SA 2.5 |
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| Mar 7, 2011 at 14:11 | history | answered | Dmitri Panov | CC BY-SA 2.5 |