2-dimensional Kähler-Einstein metrics induced by finite dimensional complex projective spaces. (English) Zbl 1487.32144
Summary: In this paper we give a complete list of non-isometric bidimensional \(S^1\)-invariant Kähler-Einstein submanifolds of a finite dimensional complex projective space endowed with the Fubini-Study metric. This solves in the aforementioned case a classical and long-staying problem addressed among others in [S.-S. Chern, J. Differ. Geom. 1, 21–31 (1967; Zbl 0168.19505); K. Tsukada, Math. Ann. 274, 503–516 (1986; Zbl 0592.53046)].
MSC:
| 32Q20 | Kähler-Einstein manifolds |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
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