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Biharmonic Lagrangian H-umbilical submanifolds in complex space forms
Abstract
We give a complete classification of proper biharmonic Lagrangian H-umbilical submanifolds in complex space forms. Such submanifolds exist only in complex projective space and are locally congruent to an explicit model obtained via the Hopf fibration. In particular, their nonexistence in complex Euclidean space provides a partial affirmative answer to Chen's conjecture.
Related
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BibTeX
@misc{sasahara2026biharmonic,
title = {{Biharmonic Lagrangian $H$-umbilical submanifolds in complex space forms}},
author = {Toru Sasahara},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32506},
eprint = {2609.32506},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32506},
}
RIS
TY - UNPB
TI - Biharmonic Lagrangian H-umbilical submanifolds in complex space forms
AU - Toru Sasahara
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32506
UR - https://arxiv.org/abs/2609.32506
AB - We give a complete classification of proper biharmonic Lagrangian H-umbilical submanifolds in complex space forms. Such submanifolds exist only in complex projective space and are locally congruent to an explicit model obtained via the Hopf fibration. In particular, their nonexistence in complex Euclidean space provides a partial affirmative answer to Chen's conjecture.
ER -