We investigate what we call generalized ovoids, that is families of totally isotropic subspaces of finite classical polar spaces such that each maximal totally isotropic subspace contains precisely one member of that family. This is a generalization of ovoids in polar spaces as well as the natural q-analog of a subcube partition of the hypercube (which can be seen as a polar space with \(q=1\)). Our main result proves that a generalized ovoid of k-spaces in polar spaces of large rank does not exist.

中文翻译：

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极空间中超立方体分区和卵形体的常见概括

我们研究所谓的广义卵形，即有限经典极空间的完全各向同性子空间族，使得每个最大完全各向同性子空间恰好包含该族的一个成员。这是极空间中卵形的推广，也是超立方体子立方体分区的自然q模拟（可以看作具有\(q=1\)的极空间）。我们的主要结果证明，大阶极空间中k空间的广义卵形不存在。