Lagrangian submanifolds attaining equality in the improved Chen's inequality

Details Lagrangian submanifolds attaining equality in the improved Chen's inequality Lagrangian submanifolds attaining equality in the improved Chen's inequality

2006-04-25

arxiv.org/abs/math/0604543v1

Mathematics

Differential Geometry

Scientific paper

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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