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Lagrangian submanifolds attaining equality in the improved Chen's inequality

John Bolton·Luc Vrancken
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Abstract

Recently Oprea gave an improved version of Chen's inequality for Lagrangian submanifolds of $\mathbb CP^n(4)$. For minimal submanifolds this inequality coincides with the original previously proved version. We consider here those non minimal 3-dimensional Lagrangian submanifolds in $\mathbb CP^3 (4)$ attaining at all points equality in the improved Chen inequality. We show how all such submanifolds may be obtained starting from a minimal Lagrangian surface in $\mathbb CP^2(4)$ and a suitable horizontal curve in $S^3(1)$.

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John Bolton, Luc Vrancken. 2006-04-25. Lagrangian submanifolds attaining equality in the improved Chen's inequality. https://arxiv.org/abs/math/0604543

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