Nonlinear Bochner-Kodaira-Nakano identity and nonlinear Hodge correspondence for morphisms

We establish a nonlinear Bochner-Kodaira-Nakano identity for sections of complex fiber bundles. As applications, we obtain a nonlinear Bochner-type vanishing theorem for holomorphic sections and a generalization of Yau's Schwarz lemma. After incorporating a nonlinear Higgs field, we derive the $D'$-