In the note we show that the conjugacy of points determined by a correlation of a space of pencils is definitionally equivalent to (suitably defined) orthogonality of lines and to a ‘polarity’, introduced in the space in question. This proves that ‘metric geometry of spaces of pencils’ can be equivalently developed as a theory of incidence enlarged by a natural (point \(\leftrightarrow \) line) or (line \(\leftrightarrow \) line) relation.
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Prażmowski, K., Żynel, M. Metric structures imposed on Grassmannians. Beitr Algebra Geom 61, 507–513 (2020). https://doi.org/10.1007/s13366-019-00480-9
- Space of pencils
- Metric projective geometry
Mathematics Subject Classification
- 51A50 (14M15)