The paper gives existence and uniqueness theorems for constant second Chern and Bismut scalar curvature metrics in fixed Hermitian conformal classes, but the proofs contain invalid maximum principle steps.
Aubin, Some nonlinear problems in Riemannian geometry, Springer Monogr
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Existence and geometry of Hermitian metrics with constant second scalar curvature
The paper gives existence and uniqueness theorems for constant second Chern and Bismut scalar curvature metrics in fixed Hermitian conformal classes, but the proofs contain invalid maximum principle steps.