scholarly journals A FLAT LAGUERRE PLANE OF KLEINEWILLINGHÖFER TYPE V

2011 ◽  
Vol 91 (2) ◽  
pp. 257-274 ◽  
Author(s):  
JEROEN SCHILLEWAERT ◽  
GÜNTER F. STEINKE
Keyword(s):  
Parameter Family ◽  
Laguerre Plane ◽  
The Other ◽  
Flat Laguerre Plane ◽  
Laguerre Planes ◽  
Type V ◽  
Central Automorphisms ◽  
Kleinewillinghöfer Type

AbstractThe Kleinewillinghöfer types of Laguerre planes reflect the transitivity properties of certain groups of central automorphisms. Polster and Steinke have shown that some of the conceivable types for flat Laguerre planes cannot exist and given models for most of the other types. The existence of only a few types is still in doubt. One of these is type V.A.1, whose existence we prove here. In order to construct our model, we make systematic use of the restrictions imposed by the group. We conjecture that our example belongs to a one-parameter family of planes all of type V.A.1.

scholarly journals Flat Laguerre planes of Kleinewillinghöfer type E obtained by cut and paste

2005 ◽  
Vol 72 (2) ◽  
pp. 213-223 ◽  
Author(s):  
Günter F. Steinke
Keyword(s):  
Laguerre Plane ◽  
Flat Laguerre Plane ◽  
Laguerre Planes ◽  
Kleinewillinghöfer Type

We provide examples of flat Laguerre planes of Kleinewillinghöfer type E, thus completing the classification of flat Laguerre planes with respect to Laguerre translations in B. Polster and G.F. Steinke, Results Maths. (2004). These planes are obtained by a method for constructing a new flat Laguerre plane from three given Laguerre planes devised in B. Polster and G. Steinke, Canad. Math. Bull. (1995) but no examples were given there.

A FAMILY OF TWO-DIMENSIONAL LAGUERRE PLANES OF KLEINEWILLINGHÖFER TYPE II.A.2

2018 ◽  
Vol 105 (3) ◽  
pp. 366-379
Author(s):  
GÜNTER F. STEINKE
Keyword(s):  
Two Dimensional ◽  
Transitive Groups ◽  
Laguerre Planes ◽  
Translation Type ◽  
Central Automorphisms ◽  
Existence Question ◽  
Kleinewillinghöfer Type

Kleinewillinghöfer classified Laguerre planes with respect to linearly transitive groups of central automorphisms. Polster and Steinke investigated two-dimensional Laguerre planes and their so-called Kleinewillinghöfer types. For some of the feasible types the existence question remained open. We provide examples of such planes of type II.A.2, which are based on certain two-dimensional Laguerre planes of translation type. With these models only one type, I.A.2, is left for which no two-dimensional Laguerre planes are known yet.

scholarly journals The inner and outer space of 2-dimensional Laguerre planes

1997 ◽  
Vol 62 (1) ◽  
pp. 104-127 ◽  
Author(s):  
B. Polster ◽  
G. F. Steinke
Keyword(s):  
Outer Space ◽  
Laguerre Plane ◽  
Generalized Quadrangles ◽  
Base Points ◽  
Laguerre Planes

AbstractThe classical 2-dimensional Laguerre plane is obtained as the geometry of non-trivial plane sections of a cylinder in R3 with a circle in R2 as base. Points and lines in R3 define subsets of the circle set of this geometry via the affine non-vertical planes that contain them. Furthemore, vertical lines and planes define partitions of the circle set via the points and affine non-vertical lines, respectively, contained in them.We investigate abstract counterparts of such sets of circles and partitions in arbitrary 2-dimensional Laguerre planes. We also prove a number of related results for generalized quadrangles associated with 2-dimensional Laguerre planes.

scholarly journals Moffatt-type flows in a trihedral cone

2013 ◽  
Vol 725 ◽  
pp. 446-461 ◽  
Author(s):  
Julian F. Scott
Keyword(s):  
Linear Combination ◽  
Particle Motion ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Parameter Family ◽  
The Other ◽  
Transient Phase ◽  
Primary Flow ◽  
Special Cases ◽  
Two Parameter

AbstractThe three-dimensional analogue of Moffatt eddies is derived for a corner formed by the intersection of three orthogonal planes. The complex exponents of the first few modes are determined and the flows resulting from the primary modes (those which decay least rapidly as the apex is approached and, hence, should dominate the near-apex flow) examined in detail. There are two independent primary modes, one symmetric, the other antisymmetric, with respect to reflection in one of the symmetry planes of the cone. Any linear combination of these modes yields a possible primary flow. Thus, there is not one, but a two-parameter family of such flows. The particle-trajectory equations are integrated numerically to determine the streamlines of primary flows. Three special cases in which the flow is antisymmetric under reflection lead to closed streamlines. However, for all other cases, the streamlines are not closed and quasi-periodic limiting trajectories are approached when the trajectory equations are integrated either forwards or backwards in time. A generic streamline follows the backward-time trajectory in from infinity, undergoes a transient phase in which particle motion is no longer quasi-periodic, before being thrown back out to infinity along the forward-time trajectory.

CHEN–GACKSTATTER TYPE SURFACES IN ${\mathbb R}_{1}^{4}$: DEFORMATION, SYMMETRY, AND THE PROBLEM OF EMBEDDEDNESS

2014 ◽  
Vol 25 (02) ◽  
pp. 1450015
Author(s):  
ZHENXIAO XIE ◽  
XIANG MA
Keyword(s):  
Uniqueness Theorem ◽  
Gaussian Curvature ◽  
Parameter Family ◽  
The Other ◽  
Other Hand ◽  
Genus One

We find a 2-parameter family of deformations in [Formula: see text] of the classical Chen–Gackstatter surface explicitly, and show the existence of a larger 4-parameter family of deformations. Each of them still has genus one, a unique end, with total Gaussian curvature - ∫ K = 8π. On the other hand, a uniqueness theorem is obtained when we assume that the surface has more than four symmetries. The problem of embeddedness is also discussed with some partial results.

Weir flows and waterfalls

1991 ◽  
Vol 230 ◽  
pp. 525-539 ◽  
Author(s):  
Frédéric Dias ◽  
E. O. Tuck
Keyword(s):  
Vertical Wall ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Parameter Family ◽  
The Other ◽  
Two Dimensional ◽  
Surface Flows ◽  
Supercritical Solutions ◽  
Subcritical Solutions ◽  
Two Parameter

Two-dimensional free-surface flows, which are uniform far upstream in a channel of finite depth that ends suddenly, are computed numerically. The ending is in the form of a vertical wall, which may force the flow upward before it falls down forever as a jet under the effect of gravity. Both subcritical and supercritical solutions are presented. The subcritical solutions are a one-parameter family of solutions, the single parameter being the ratio between the height of the wall and the height of the uniform flow far upstream. On the other hand, the supercritical solutions are a two-parameter family of solutions, the second parameter being the Froude number. Moreover, for some combinations of the parameters, it is shown that the solution is not unique.

scholarly journals Bianchi Type-V Bulk Viscous Cosmic String inf(R,T)Gravity with Time Varying Deceleration Parameter

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Bïnaya K. Bishi ◽  
K. L. Mahanta
Keyword(s):  
Deceleration Parameter ◽  
Bianchi Type ◽  
Cosmic Strings ◽  
The Other ◽  
Time Varying ◽  
Constant Deceleration Parameter ◽  
Linearly Varying Deceleration Parameter ◽  
Bulk Viscous ◽  
Type V ◽  
Bianchi Type V

We study the Bianchi type-V string cosmological model with bulk viscosity inf(R,T)theory of gravity by considering a special form and linearly varying deceleration parameter. This is an extension of the earlier work of Naidu et al., 2013, where they have constructed the model by considering a constant deceleration parameter. Here we find that the cosmic strings do not survive in both models. In addition we study some physical and kinematical properties of both models. We observe that in one of our models these properties are identical to the model obtained by Naidu et al., 2013, and in the other model the behavior of these parameters is different.

Central Automorphisms Of Laguerre Planes

1998 ◽  
Vol 31 (4) ◽  
Author(s):  
H. Makowiecka ◽  
A. Matraś
Keyword(s):  
Laguerre Planes ◽  
Central Automorphisms

scholarly journals A family of 2-dimensional Laguerre planes of generalised shear type

2000 ◽  
Vol 61 (1) ◽  
pp. 69-83 ◽  
Author(s):  
B. Polster ◽  
G. F. Steinke
Keyword(s):  
Shear Type ◽  
Laguerre Planes ◽  
Central Automorphisms

We construct a family of 2-dimensional Laguerre planes that generalises ovoidal Laguerre planes and the Laguerre planes of shear type, as described by Löwen and Pfüller, by gluing together circle sets from up to eight different ovoidal Laguerre planes. Each plane in this family admits all maps (x, y) ↦ (x, ry) for r > 0 as central automorphisms at the circle y = 0.

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