A Class of Topological Affine Translation Planes Having no Topological Projective Extension

1993 ◽  
Vol 23 (3-4) ◽  
pp. 294-302 ◽  
Author(s):  
Eberhard Eisele
Keyword(s):  
Translation Planes ◽  
Projective Extension ◽  
Affine Translation ◽  
Topological Affine

Unitals in Topological Affine Translation Planes Need Not Be Strictly Convex

2003 ◽  
Vol 139 (4) ◽  
pp. 275-284
Author(s):  
Harald L�we ◽  
Rainer L�wen ◽  
Emine Soyt�rk
Keyword(s):  
Translation Planes ◽  
Strictly Convex ◽  
Affine Translation ◽  
Topological Affine

scholarly journals On collineation groups of translation planes of orderq4

1986 ◽  
Vol 9 (3) ◽  
pp. 617-620
Author(s):  
V. Jha ◽  
N. L. Johnson
Keyword(s):  
Translation Plane ◽  
Translation Planes ◽  
Nonsolvable Group ◽  
Translation Complement ◽  
Affine Translation ◽  
Collineation Groups ◽  
Affine Translation Plane

LetPbe an affine translation plane of orderq4admitting a nonsolvable groupGin its translation complement. IfGfixes more thanq+1slopes, the structure ofGis determined. In particular, ifGis simple thenqis even andG=L2(2s)for some integersat least2.

Ovoids and Translation Planes

1982 ◽  
Vol 34 (5) ◽  
pp. 1195-1207 ◽  
Author(s):  
William M. Kantor
Keyword(s):  
Vector Space ◽  
Singular Points ◽  
The Other ◽  
Translation Planes ◽  
Orthogonal Vector ◽  
Other Hand ◽  
Affine Translation

An ovoid in an orthogonal vector space V of type Ω+(2n, q) or Ω(2n – 1, q) is a set Ω of qn–1 + 1 pairwise non-perpendicular singular points. Ovoids probably do not exist when n > 4 (cf. [12], [6]) and seem to be rare when n = 4. On the other hand, when n = 3 they correspond to affine translation planes of order q2, via the Klein correspondence between PG(3, q) and the Ω+(6, q) quadric.In this paper we will describe examples having n = 3 or 4. Those with n = 4 arise from PG(2, q3), AG(2, q3), or the Ree groups. Since each example with n = 4 produces at least one with n = 3, we are led to new translation planes of order q2.

On Translation Planes which Admit Solvable Autotopism Groups Having a Large Slope Orbit

1984 ◽  
Vol 36 (5) ◽  
pp. 769-782 ◽  
Author(s):  
Vikram Jha
Keyword(s):  
Translation Plane ◽  
Collineation Group ◽  
Affine Plane ◽  
Translation Planes ◽  
Hall Plane ◽  
Autotopism Group ◽  
Affine Translation ◽  
Planar Group ◽  
Affine Translation Plane

Our main object is to prove the following result.THEOREM C. Let A be an affine translation plane of order qr ≧ q2 suchthatl∞, the line at infinity, coincides with the translation axis of A. Suppose G is a solvable autotopism group of A that leaves invariant a set Δ of q + 1 slopes and acts transitively on l∞ \ Δ.Then the order of A is q2.An autotopism group of any affine plane A is a collineation group G that fixes at least two of the affine lines of A; if in fact the fixed elements of G form a subplane of A we call G a planar group. When A in the theorem is a Hall plane [4, p. 187], or a generalized Hall plane ([13]), G can be chosen to be a planar group.

Compact spreads and compact translation planes over locally compact fields

1989 ◽  
Vol 36 (1-2) ◽  
pp. 110-116 ◽  
Author(s):  
Rainer L�wen
Keyword(s):  
Translation Planes ◽  
Locally Compact

On the compatibility of planar and nonplanar involutions in translation planes

1982 ◽  
Vol 52 (1) ◽  
pp. 16-28 ◽  
Author(s):  
Norman L. Johnson
Keyword(s):  
Translation Planes

Translation planes admitting many homologies

1994 ◽  
Vol 49 (1-2) ◽  
pp. 117-149 ◽  
Author(s):  
Norman L. Johnson ◽  
Rolando Pomareda
Keyword(s):  
Translation Planes

Weingarten Affine Translation Surfaces in Euclidean 3-Space

2017 ◽  
Vol 72 (4) ◽  
pp. 1839-1848 ◽  
Author(s):  
Seoung Dal Jung ◽  
Huili Liu ◽  
Yixuan Liu
Keyword(s):  
Translation Surfaces ◽  
Affine Translation

Unitals in Translation Planes

2007 ◽  
pp. 671-682
Keyword(s):  
Translation Planes
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