Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.32506

Author: Sasahara, Toru

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214796460

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