Year: 2026
Type: preprint
Abstract: 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 $D'$-$D''$ and $D^c$-$D$ identities. Under natural Hamiltonian and compactness assumptions, these identities imply that a section of a nonlinear harmonic bundle is flat if and only if it is a Higgs section with vanishing degree. We extend this correspondence first to sub-fibrations and then, via the graph construction, to morphisms.
Source: arXiv (Cornell University)
Authors: Li, Nianzi, Sheng, Mao
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168833627