Abstract
We prove that the complex projective space equipped with its Fubini-Study metric admits no compact Kähler-Einstein submanifold with nonpositive Einstein constant. In particular, the Calabi-Yau metrics carried by an algebraic K3 surface cannot be realized by projective embeddings.
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References
Bochner, S. Curvature in hermitian metric,Bull. Am. Math. Soc.,53, 179–185, (1947).
Borel, A.Linear Algebraic Groups, Benjamin, New York, 1969.
Bouche, T. Convergence de la métrique de Fubini-Study d’un fibré linéaire positif,Ann. Inst. Fourier Grenoble,40(1), 117–130,(1990).
Bourguignon, J.-P. Géométrie riemannienne en dimension 4, (A.L. Besse), ch. VIII, Cedic-Nathan, Paris, 1981.
Calabi, E. Isometric embedding of complex manifolds,Ann. Math.,58, 1–23, (1953).
Serre, J.-P. Représentations linéaires et espaces homogènes kähleriens des groupes de Lie compacts, Séminaire Bourbaki 1954, Benjamin, 1966.
Tian, G. On a set of polarized Kähler metrics on algebraic manifolds,J. Diff. Geom.,32, 99–130, (1990).
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Communicated by Peter Li
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Hulin, D. Kähler-Einstein metrics and projective embeddings. J Geom Anal 10, 525–528 (2000). https://doi.org/10.1007/BF02921947
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DOI: https://doi.org/10.1007/BF02921947