On complexes of projective rotation and complexes with a quadruple inflection center on each ray in three-dimensional projective space

1973 ◽  
Vol 25 (2) ◽  
pp. 161-171
Author(s):  
N. I. Kovantsov ◽  
V. G. Ponomarev
Keyword(s):  
Projective Space ◽  
Three Dimensional ◽  
Dimensional Projective Space

Transformations depending on sets of associated points

1952 ◽  
Vol 48 (3) ◽  
pp. 383-391
Author(s):  
T. G. Room
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Three Dimensional ◽  
Cubic Curves ◽  
Birational Transformations ◽  
Quadric Surfaces ◽  
Base Points ◽  
Dimensional Projective Space ◽  
Quartic Curves

This paper falls into three sections: (1) a system of birational transformations of the projective plane determined by plane cubic curves of a pencil (with nine associated base points), (2) some one-many transformations determined by the pencil, and (3) a system of birational transformations of three-dimensional projective space determined by the elliptic quartic curves through eight associated points (base of a net of quadric surfaces).

scholarly journals Classification of 3T1R Parallel Manipulators Based on Their Wrench Graph

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Semaan Amine ◽  
Ossama Mokhiamar ◽  
Stéphane Caro
Keyword(s):  
Projective Space ◽  
Parallel Manipulator ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Geometrical Properties ◽  
Cayley Algebra ◽  
Dimensional Projective Space ◽  
Grassmann Cayley Algebra

This paper presents a classification of 3T1R parallel manipulators (PMs) based on the wrench graph. By using the theory of reciprocal screws, the properties of the three-dimensional projective space, the wrench graph, and the superbracket decomposition of Grassmann–Cayley algebra, six typical wrench graphs for 3T1R parallel manipulators are obtained along with their singularity conditions. Furthermore, this paper shows a way in which each of the obtained typical wrench graphs can be used in order to synthesize new 3T1R parallel manipulator architectures with known singularity conditions and with an understanding of their geometrical properties and assembly conditions.

scholarly journals On principal surfaces of quasi-special complexes with twofold fibration in $P_3$

1987 ◽  
pp. 120
Author(s):  
Ye.N. Ishchenko
Keyword(s):  
Projective Space ◽  
Three Dimensional ◽  
Dimensional Projective Space ◽  
Principal Surfaces

We prove that, if one of principal surfaces of quasi-special complexes with twofold fibration in three-dimensional projective space $P_3$ is a quadric, then this complex is complemented by second complex, which allows twofold fibration as well.

scholarly journals A quadratic transformation of the three-dimensional space of all conics through two points of a projective plane

2009 ◽  
Vol 42 (3) ◽  
Author(s):  
Giorgio Donati
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Other ◽  
Quadratic Transformation ◽  
Pencil Of Conics ◽  
Dimensional Projective Space ◽  
Three Dimensional Space

AbstractUsing the Steiner’s method of projective generation of conics and its dual we define two projective mappings of a double contact pencil of conics into itself and we prove that one is the inverse of the other. We show that these projective mappings are induced by quadratic transformations of the three-dimensional projective space of all conics through two distinct points of a projective plane.

THE INVARIANT MEASURES AT WEAK DISORDER FOR THE TWO-LINE ANDERSON MODEL

2004 ◽  
Vol 16 (05) ◽  
pp. 639-673
Author(s):  
T. C. DORLAS ◽  
J. V. PULÉ
Keyword(s):  
Projective Space ◽  
Anderson Model ◽  
Invariant Measures ◽  
Three Dimensional ◽  
Weak Disorder ◽  
Single Chain ◽  
Zero Energy ◽  
Dimensional Projective Space

We study the invariant measures in the weak disorder limit, for the Anderson model on two coupled chains. These measures live on a three-dimensional projective space, and we use a total set of functions on this space to characterize the measures. We find that at several points of the spectrum, there are anomalies similar to that first found by Kappus and Wegner for the single chain at zero energy.

scholarly journals THEOREMS OF POINTS AND PLANES IN THREE-DIMENSIONAL PROJECTIVE SPACE

2010 ◽  
Vol 88 (1) ◽  
pp. 75-92 ◽  
Author(s):  
DAVID G. GLYNN
Keyword(s):  
Graph Theory ◽  
Projective Space ◽  
Search Algorithm ◽  
Three Dimensional ◽  
Point Configuration ◽  
Graph Theoretic ◽  
Dimensional Projective Space ◽  
Forbidden Minors

AbstractWe discuss n4 configurations of n points and n planes in three-dimensional projective space. These have four points on each plane, and four planes through each point. When the last of the 4n incidences between points and planes happens as a consequence of the preceding 4n−1 the configuration is called a ‘theorem’. Using a graph-theoretic search algorithm we find that there are two 84 and one 94 ‘theorems’. One of these 84 ‘theorems’ was already found by Möbius in 1828, while the 94 ‘theorem’ is related to Desargues’ ten-point configuration. We prove these ‘theorems’ by various methods, and connect them with other questions, such as forbidden minors in graph theory, and sets of electrons that are energy minimal.

scholarly journals Proving and Generalizing Desargues’ Two-Triangle Theorem in 3-Dimensional Projective Space

Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Dimitrios Kodokostas
Keyword(s):  
Projective Space ◽  
Arbitrary Number ◽  
Three Dimensional ◽  
3 Dimensional ◽  
Dimensional Projective Space ◽  
Set Of Points

With the use of only the incidence axioms we prove and generalize Desargues’ two-triangle Theorem in three-dimensional projective space considering an arbitrary number of points on each one of the two distinct planes allowing corresponding points on the two planes to coincide and three points on any of the planes to be collinear. We provide three generalizations and we define the notions of a generalized line and a triangle-connected plane set of points.

Normal quintic surfaces with Kodaira dimension one

2015 ◽  
Vol 26 (02) ◽  
pp. 1550015
Author(s):  
Yumiko Umezu
Keyword(s):  
Projective Space ◽  
Three Dimensional ◽  
Kodaira Dimension ◽  
Elliptic Surfaces ◽  
Base Curve ◽  
Dimensional Projective Space ◽  
Dimension One

We study normal quintic surfaces in the three-dimensional projective space whose nonsingular models are surfaces of Kodaira dimension one. It turns out that the genus of the base curve of their elliptic fibration is equal to 0 or 1, and the possible values of other invariants of these surfaces and the singularities on them are obtained. We give several examples to show the existence of such surfaces. Moreover we determine the defining equations of general quintic surfaces whose nonsingular models are irregular elliptic surfaces of Kodaira dimension one.

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