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arXiv · 2609.32506

Biharmonic Lagrangian $H$-umbilical submanifolds in complex space forms

Toru Sasahara
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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.

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Toru Sasahara. 2026-09-26. Biharmonic Lagrangian $H$-umbilical submanifolds in complex space forms. https://arxiv.org/abs/2609.32506

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