# Adjacency preserving mappings

@article{Huang2003AdjacencyPM,
author={Wen-ling Huang and Andreas E. Schroth},
year={2003},
volume={3}
}
• Published 9 January 2003
• Mathematics
• Advances in Geometry
In a certain class of point-line geometries, called locally projective near polygons, which includes dual polar spaces and generalised 2n-gons, surjective adjacency preserving mappings are already collineations.
5 Citations
Innovations in Incidence Geometry
In certain point-line geometries G = (P,L), G′ = (P ′,L′), which include dense near polygons and the geometry of Hermitian matrices, any adjacency preserving mapping φ : P → P ′ satisfying ∃p, q ∈ P
Adjacency preserving mappings of 2 × 2 Hermitian matrices
Summary.We determine all mappings φ from the space of 2 × 2 Hermitian matrices which take pairs of adjacent matrices to pairs of adjacent matrices and such that the image of φ contains two matrices
Adjacency preserving mappings on real symmetric matrices
Let Sn denote the space of all n × n real symmetric matrices. For n ≥ 2 we characterize maps Φ : Sn → Sm, which preserve adjacency, i.e. if A,B ∈ Sn and rank (A−B) = 1, then rank (Φ(A)−Φ(B)) = 1.
Adjacency preserving mappings on real symmetric matrices
Let $S_{n}$ denote the space of all $n \times n$ real symmetric matrices. For n=2 or n>2 we characterize maps F from $S_{n}$ to $S_{m}$ which preserve adjacency, i.e. if rank(A-B)=1, then
Adjacency preserving mappings of symmetric and hermitian matrices
• Mathematics
• 2004
Summary. Let D be a division ring with an involution $$\overline{\phantom{e}}$$ and $$F = \{a \in D \mid \overline{a} = a\}$$ . When $$\overline{\phantom{e}}$$ is the identity map then D

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في هذا البحث نتناول الفراغات القطبية العامة ذات دليل ويت Witt index الذي قيمته على الأقل ثلاثة بفرض أن π :S(ξ)→s (ξ)هي تجمع كثيف (a thick collineation) بين فراغات قطبية ذات i(ξ) =i(ξ)≥3 فانه يوجد
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