1. On a generalized notion of metrics.
- Author
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Beyn, Wolf-Jürgen
- Subjects
- *
EUCLIDEAN geometry , *GRASSMANN manifolds , *VECTOR spaces , *CALCULUS , *HYPERGRAPHS - Abstract
In these notes we generalize the notion of a (pseudo) metric measuring the distance of two points, to a (pseudo) n-metric which assigns a value to a tuple of n ≥ 2 points. Some elementary properties of pseudo n-metrics are provided and their construction via exterior products is investigated. We discuss some examples from the geometry of Euclidean vector spaces leading to pseudo n-metrics on the unit sphere, on the Stiefel manifold, and on the Grassmann manifold. Further, we construct a pseudo n-metric on hypergraphs and discuss the problem of generalizing the Hausdorff metric for closed sets to a pseudo n-metric. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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