Generating quadrangulations of surfaces with minimum degree at least 3

In this article, we show that all quadrangulations of the sphere with minimum degree at least 3 can be constructed from the pseudo‐double wheels, preserving the minimum degree at least 3, by a sequence of two kinds of transformations called “vertex‐splitting” and “4‐cycle addition.” We also consider such generating theorems for other closed surfaces. These theorems can be translated into those of 4‐regular graphs on surfaces by taking duals. © 1999 John Wiley & Sons, In. J Graph Theory 30: 223–234, 1999     

(Semi-)Riemannian geometry of (para-)octonionic projective planes

We use reduced homogeneous coordinates to construct and study the (semi-)Riemannian geometry of the octonionic (or Cayley) projective plane , the octonionic projective plane of indefinite signature , the para-octonionic (or split octonionic) projective plane and the hyperbolic dual of the octonionic projective plane . We also show that our manifolds are isometric to the (para-)octonionic projective planes defined classically by quotients of Lie groups.     

Projective Planes of Order q whose Collineation Groups have Order q 2

Translation planes of order q are constructed whose full collineation groups have order q ².     

Smooth Projective Planes

Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to . We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plane curves are smooth collineations, and prove a variety of results analogous to the theory of classical projective planes. *Thanks to Robert Bryant and John Franks.     

关于Suzuki群与射影平面的一个注记

设G Aut(D)且Soc(G) =Sz(q) ,这里q=2 p,p为奇素数,若有Sz(q) 相似文献   

A Combinatorial Characterization of Hermitian Curves

A unital U with parameter q is a 2 – (q ³ + 1, q + 1, 1) design. If a point set U in PG(2, q ²) together with its (q + 1)-secants forms a unital, then U is called a Hermitian arc. Through each point p of a Hermitian arc H there is exactly one line L having with H only the point p in common; this line L is called the tangent of H at p. For any prime power q, the absolute points and nonabsolute lines of a unitary polarity of PG(2, q ²) form a unital that is called the classical unital. The points of a classical unital are the points of a Hermitian curve in PG(2, q ²).Let H be a Hermitian arc in the projective plane PG(2, q ²). If tangents of H at collinear points of H are concurrent, then H is a Hermitian curve. This result proves a well known conjecture on Hermitian arcs.