Toric Kähler-Einstein manifolds immersed in complex projective spaces

Differential Geometry and its Applications 2026 Open access

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Authors: Gianni Manno, Filippo Salis
DOI: 10.1016/j.difgeo.2026.102347
Cited by: 0
References: 38

Abstract

We give a complete list, for n ≤ 6 , of mutually non-isometric T n -invariant Kähler-Einstein manifolds, where T n is the real n -dimensional torus, immersed in a finite dimensional complex projective space endowed with the Fubini-Study metric. This class includes, in particular, all toric Kähler manifolds. This solves, in the aforementioned case, a classical and long-staying problem addressed among others by Calabi and Chern.

Fields of Study & Subjects

Geometry and complex manifolds Geometric Analysis and Curvature Flows Black Holes and Theoretical Physics

Publication details

Journal / source
Differential Geometry and its Applications
Publisher
Elsevier BV
Volume
103
Pages
102347–102347
Publication date
17 February 2026
Language
EN