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Nonlinear Bochner-Kodaira-Nakano identity and nonlinear Hodge correspondence for morphisms
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 Dc-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.
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BibTeX
@misc{li2026nonlinear,
title = {{Nonlinear Bochner-Kodaira-Nakano identity and nonlinear Hodge correspondence for morphisms}},
author = {Nianzi Li and Mao Sheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.13450},
eprint = {2607.13450},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.13450},
}
RIS
TY - UNPB
TI - Nonlinear Bochner-Kodaira-Nakano identity and nonlinear Hodge correspondence for morphisms
AU - Nianzi Li
AU - Mao Sheng
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2607.13450
UR - https://arxiv.org/abs/2607.13450
AB - 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.
ER -