New York Journal of Mathematics
Volume 28 (2022), 420-432


Gianni Manno and Filippo Salis

2-dimensional Kähler-Einstein metrics induced by finite dimensional complex projective spaces

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Published: February 15, 2022.
Keywords: Kähler-Einstein metrics; Kähler immersions; Kähler toric manifolds; complex projective spaces; flag manifolds; Calabi's diastasis function.
Subject: 32Q20; 53C55; 35J96; 35C11.

In this paper we give a complete list of non-isometric bidimensional S1-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 [7] and [31].


The authors gratefully acknowledge support by the project "Connessioni proiettive, equazioni di Monge-Ampere e sistemi integrabili" (INdAM), "MIUR grant Dipartimenti di Eccellenza 2018-2022 (E11G18000350001)", PRIN project 2017 "Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics" (code 2017JZ2SW5) and the "Finanziamento alla Ricerca (53_RBA17MANGIO)". The authors are members of GNSAGA of INdAM

Author information

Gianni Manno:
Dipartimento di Scienze Matematiche "G. L. Lagrange"
Politecnico di Torino
Corso Duca degli Abruzzi 24, 10129 Torino, Italy


Filippo Salis:
Istituto Nazionale di Alta Matematica "F. Severi"
Politecnico di Torino
Corso Duca degli Abruzzi 24, 10129 Torino, Italy