Explicit Fefferman-Szegő metric on egg domains D_{2m} is Kähler-Einstein and proportional to Bergman metric iff m=1.
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The invariant Szeg\H{o} metric on Egg domains
Explicit Fefferman-Szegő metric on egg domains D_{2m} is Kähler-Einstein and proportional to Bergman metric iff m=1.