Tohoku Mathematical Journal
2026
March
SECOND SERIES VOL. 78, NO. 1

Tohoku Math. J.
78 (2026), 31-45

Title SEGRE EMBEDDING AND BIHARMONICITY

Dedicated to Professor Bang--Yen Chen on the occasion of his 80th birthday
Author Hiba Bibi, Dorel Fetcu and Cezar Oniciuc

(Received January 10, 2024, revised March 15, 2024)
Abstract. We consider the Segre embedding of the product $\mathbb{C}P^p\times\mathbb{C}P^q$ into $\mathbb{C}P^{p+q+pq}$ and study the biharmonicity of $M^p\times\mathbb{C}P^q$ and $M^p_1\times M^q_2$ as submanifolds of $\mathbb{C}P^{p+q+pq}$, where $M$ and $M_1$ are Lagrangian submanifolds of $\mathbb{C}P^p$ and $M_2$ is a Lagrangian submanifold of $\mathbb{C}P^q$. We find two new large classes of biharmonic submanifolds in complex projective space forms.

Mathematics Subject Classification. Primary 32V40; Secondary 53C40, 31B30, 53C42.
Key words and phrases. Biconservative submanifolds, biharmonic submanifolds, Segre embedding.

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