We study the projective behavior, mainly with respect to osculating spaces and secant varieties, of Lagrangian Grassmannians and Spinor varieties. In particular, we give numerical conditions ensuring the non secant defectivity of Lagrangian Grassmannians in their Plücker embedding and of Spinor varieties in both their Plücker and Spinor embeddings.

中文翻译：

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Lagrangian Grassmannians和Spinor品种的几何投影方面

我们研究了投影行为，主要是关于拉格朗日草曼和斯宾诺变种的密合空间和割线变种。特别是，我们给出了数值条件，以确保拉格朗日草曼在其Plücker嵌入中以及Spinor变种在其Plücker和Spinor嵌入中的非割线缺陷。