Higher K-energy functionals and higher Futaki invariants

2002/04/23 by Ben Weinkove, Weinkove, Ben
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.math/0204271

14 pages, Latex; references added, Theorem 2 corrected

openalex publication_date 2002/04/23 · arxiv created 2002/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note discusses the higher K-energy functionals which were defined by Bando and Mabuchi, and integrate higher Futaki invariants. Two new formulas for the higher K-energy functionals are given, and the second K-energy is shown to be related to Donaldson's Lagrangian applied to metrics on the tangent bundle.

Related

• A new formula for the energy functionals E_k and its applications
• K Energy and K stability on Hypersurfaces
• The Futaki invariant and the Mabuchi energy of a complete intersection
• A criterion for the properness of the K-energy in a general Kahler class (II)
• Extremal metrics and lower bound of the modified K-energy