Toric para-Kaehler-Einstein manifolds immersed in para-Kaehler space forms

2025/10/22 by Gianni Manno, Manno, Gianni, Filippo Salis +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2510.19625

openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

A classical and long-staying problem addressed, among others, by Calabi and Chern, is that to find a complete list of mutually non-isometric Kaehler-Einstein manifolds immersed in a finite-dimensional Kaehler space form. We address the same problem in the para-Kaehler context and, then, we find a list of mutually non-isometric toric para-Kaehler manifolds analytically immersed in a finite-dimensional para-Kaehler space form

Citations

• Kähler immersions of Kähler manifolds into complex space forms
• Projectively induced rotation invariant Kähler metrics
• Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties
• On Homothetic Balanced Metrics
• Homogeneous para-Kähler Einstein manifolds

Related

• \mathbbTⁿ-invariant Kaehler-Einstein manifolds immersed in complex projective spaces
• Para-Kaehler immersions in para-Kaehler space forms
• Toric extremal Kaehler-Ricci solitons are Kaehler-Einstein
• Anti-Kaehlerian Manifolds
• Examples of non-symmetric Kähler-Einstein toric Fano manifolds