A Weil-Petersson type metric on the space of Fano Kähler-Ricci solitons

DOI10.1007/s12220-022-01030-xOpenAlexW4297894284MaRDI QIDQ2082297

Yingying Zhang, Huai-Dong Cao, Xiaofeng Sun

Publication date: 4 October 2022

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.15627

zbMATH Keywords

Kähler-Ricci solitonsWeil-Petersson metricdeformation of complex structurestwisted Kuranishi-divergence gauge

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15) Deformations of special (e.g., CR) structures (32G07)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Deformation of canonical metrics. I
• Asymptotic curvature of moduli spaces for Calabi-Yau threefolds
• A new holomorphic invariant and uniqueness of Kähler-Ricci solitons
• Sectional curvatures of Kähler moduli
• The moduli space of extremal compact Kähler manifolds and generalized Weil-Petersson metrics
• Einstein metrics and complex structures
• Weil-Petersson metric in the moduli space of compact polarized Kähler- Einstein manifolds of zero first Chern class
• Chern forms and the Riemann tensor for the moduli space of curves
• Kähler-Einstein metrics and integral invariants
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• The Weil-Petersson geometry of the moduli space of SU(n\(\geq 3)\) (Calabi- Yau) manifolds. I
• A theorem of Calabi-Matsushima's type
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• On deformations of Fano manifolds
• Kähler-Ricci soliton and \(H\)-functional
• Some remarks on Teichmüller's space of Riemann surfaces
• Curvature properties of Teichmüller's space
• Recent Progress on Ricci Solitons
• A moment map interpretation of the Ricci form, K\"ahler--Einstein structures, and Teichm\"uller spaces
• The Ding Functional, Berndtsson Convexity and Moment Maps
• Existence of Gradient Kahler-Ricci Solitons