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arXiv · 2601.18504

Curvature and Lagrangian submanifolds of the homogeneous nearly K\"ahler $\mathbb{C}P^3$

Michaël Liefsoens·Joeri Van der Veken
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Abstract

A tractable definition of the homogeneous nearly K\"ahler structure on $\mathbb{C}P^3$ is given via the Hopf fibration, facilitating explicit computations and analysis. The description extends to all homogeneous metrics on $\mathbb{C}P^3$, providing expressions for their Riemann curvature tensors and full isometry groups. Rigid immersions are presented for all extrinsically homogeneous Lagrangian submanifolds in the nearly K\"ahler $\mathbb{C}P^3$, and the nonexistence of Lagrangians with constant sectional curvature is established.

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Michaël Liefsoens, Joeri Van der Veken. 2026-01-26. Curvature and Lagrangian submanifolds of the homogeneous nearly K\"ahler $\mathbb{C}P^3$. https://arxiv.org/abs/2601.18504

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