2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63884This 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.14 pages, Latex; references added, Theorem 2 correctedDifferential Geometrytext