Kaehler-Ricci solitons on homogeneous toric bundles (I)

2006/04/04 by Fabio Podestà, Podesta', Fabio, Andrea Spiro +1
Mathematics · Physics and Astronomy · #14M15 #32M12 #53C55 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0604070

openalex publication_date 2006/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the first of a sequence of two papers. Here, a simple algebraic characterization of the Fano manifolds in the class of homogeneous toric bundles over a flag manifold G^C/P is provided in terms of symplectic data. The result of this paper is used in the second paper, where it is proved that an homogeneous toric bundle over a flag manifold admits a Kaehler-Ricci solitonic metric if and only if it is Fano.

Related

• Kaehler-Ricci solitons on homogeneous toric bundles (II)
• Homogeneous toric bundles with positive first Chern class
• Kähler-Ricci solitons on toric Fano orbifolds
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• The moduli space of Fano manifolds with Kähler-Ricci solitons