We introduce new pseudo-metrics on spaces of Lagrangian submanifolds of a symplectic manifold $(M,\omega)$ by considering areas associated to projecting Lagrangian cobordisms in $\mathbb{C} \times M$ to the "time-energy plane" $\mathbb{C}$. We investigate the non-degeneracy properties of these pseudo-metrics, reflecting the rigidity and flexibility aspects of Lagrangian cobordisms.

中文翻译：

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拉格朗日坐标和度量不变量

我们通过考虑与将 $\mathbb{C} \times M$ 中的拉格朗日坐标投影到“时间-能量平面”相关的区域，在辛流形 $(M,\omega)$ 的拉格朗日子流形空间上引入新的伪度量$\mathbb{C}$。我们研究了这些伪度量的非简并性，反映了拉格朗日协边的刚性和灵活性方面。