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On a generalized notion of metrics.
- Source :
-
Aequationes Mathematicae . Aug2024, Vol. 98 Issue 4, p953-977. 25p. - Publication Year :
- 2024
-
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]
- Subjects :
- *EUCLIDEAN geometry
*GRASSMANN manifolds
*VECTOR spaces
*CALCULUS
*HYPERGRAPHS
Subjects
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 98
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 178837547
- Full Text :
- https://doi.org/10.1007/s00010-024-01092-y