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PreprintCC BY 4.0arXiv

Biharmonic submanifolds in nonpositive space forms

  • Yu Fu
  • Min-chun Hong
  • Dan Yang
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Abstract

We prove that there are no proper biharmonic submanifolds with parallel normalized mean curvature vector field in a nonpositive space form, in arbitrary dimension and codimension. We also prove that every biharmonic surface with flat normal bundle in a four-dimensional nonpositive space form is minimal. These results provide substantial support for Chen's conjecture and the generalized Chen's conjecture for hyperbolic space in higher codimensions.

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Cite

BibTeXRIS
BibTeX
@misc{fu2026biharmonic,
  title = {{Biharmonic submanifolds in nonpositive space forms}},
  author = {Yu Fu and Min-chun Hong and Dan Yang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04159},
  eprint = {2611.04159},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04159},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Biharmonic submanifolds in nonpositive space forms
AU  - Yu Fu
AU  - Min-chun Hong
AU  - Dan Yang
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04159
UR  - https://arxiv.org/abs/2611.04159
AB  - We prove that there are no proper biharmonic submanifolds with parallel normalized mean curvature vector field in a nonpositive space form, in arbitrary dimension and codimension. We also prove that every biharmonic surface with flat normal bundle in a four-dimensional nonpositive space form is minimal. These results provide substantial support for Chen's conjecture and the generalized Chen's conjecture for hyperbolic space in higher codimensions.
ER  -