\mathbbTⁿ-invariant Kaehler-Einstein manifolds immersed in complex projective spaces

2024/07/17 by Manno, Gianni, Salis, Filippo
#32Q20 #32Q40 #35C11 #35J96 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.12685

Abstract

We give a complete list, for n ≤ 6, of non-isometric \mathbbTⁿ-invariant Kaehler-Einstein manifolds immersed in 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 by Calabi and Chern.

Related

• Toric para-Kaehler-Einstein manifolds immersed in para-Kaehler space forms
• Projectively induced rotation invariant Kähler metrics
• Lower dimensional S¹-invariant Kähler-Einstein metrics via integrable structures
• Kähler-Einstein toric submanifolds of the projective space
• Anti-Kaehlerian Manifolds