On the lower bounds of the L^2-norm of the Hermitian scalar curvature

Julien Keller (1) , Mehdi Lejmi

1 I2M - Institut de Mathématiques de Marseille

On a pre-quantized symplectic manifold, we show that the symplectic Futaki invariant, which is an obstruction to the existence of constant Hermitian scalar curvature almost-Kähler metrics, is actually an asymptotic invariant. This allows us to deduce a lower bound for the L^2-norm of the Hermitian scalar curvature as obtained by S. Donaldson \cite{Don} in the Kähler case.

Domaines: Géométrie différentielle [math.DG]

Julien Keller, Mehdi Lejmi. On the lower bounds of the L^2-norm of the Hermitian scalar curvature. Journal of Symplectic Geometry, 2019, 18 (2), pp.537-558. ⟨hal-01481895⟩