Adjacency preserving mappings

@article{Huang2003AdjacencyPM,
  title={Adjacency preserving mappings},
  author={Wen-ling Huang and Andreas E. Schroth},
  journal={Advances in Geometry},
  year={2003},
  volume={3}
}
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. 
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
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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