scholarly journals Compact Quotient Manifolds of Domains in a Complex 3-Dimensional Projective Space and the Lebesgue Measure of Limit Sets

1996 ◽  
Vol 19 (1) ◽  
pp. 99-119 ◽  
Author(s):  
Masahide KATO
Keyword(s):  
Projective Space ◽  
Lebesgue Measure ◽  
Limit Sets ◽  
3 Dimensional ◽  
Compact Quotient ◽  
Dimensional Projective Space

Maximal Strictly Partial Spreads

1978 ◽  
Vol 30 (03) ◽  
pp. 483-489 ◽  
Author(s):  
Gary L. Ebert
Keyword(s):  
Projective Space ◽  
Partial Spread ◽  
3 Dimensional ◽  
Partial Spreads ◽  
Maximal Partial Spread ◽  
Dimensional Projective Space

Let ∑ = PG(3, q) denote 3-dimensional projective space over GF(q). A partial spread of ∑ is a collection W of pairwise skew lines in ∑. W is said to be maximal if it is not properly contained in any other partial spread. If every point of ∑ is contained in some line of W, then W is called a spread. Since every spread of PG(3, q) consists of q2 + 1 lines, the deficiency of a partial spread W is defined to be the number d = q2 + 1 — |W|. A maximal partial spread of ∑ which is not a spread is called a maximal strictly partial spread (msp spread) of ∑.

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.

scholarly journals LINKING NUMBER IN A PROJECTIVE SPACE AS THE DEGREE OF A MAP

2007 ◽  
Vol 16 (04) ◽  
pp. 489-497 ◽  
Author(s):  
JULIA VIRO DROBOTUKHINA
Keyword(s):  
Projective Space ◽  
Configuration Space ◽  
The Self ◽  
Real Projective Space ◽  
3 Dimensional ◽  
Linking Number ◽  
Degree Of A Map ◽  
Number Of Cycles ◽  
Dimensional Projective Space

For any two disjoint oriented circles embedded into the 3-dimensional real projective space, we construct a 3-dimensional configuration space and its map to the projective space such that the linking number of the circles is the half of the degree of the map. Similar interpretations are given for the linking number of cycles in a projective space of arbitrary odd dimension and the self-linking number of a zero homologous knot in the 3-dimensional projective space.

Constraint and Singularity Analysis of Lower-Mobility Parallel Manipulators With Parallelogram Joints

2010 ◽  
Author(s):  
Semaan Amine ◽  
Daniel Kanaan ◽  
Ste´phane Caro ◽  
Philippe Wenger
Keyword(s):  
Projective Space ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
3 Dimensional ◽  
Geometric Conditions ◽  
Constraint Analysis ◽  
Lower Mobility ◽  
Dimensional Projective Space ◽  
Grassmann Cayley Algebra

This paper presents a general approach to analyze the singularities of lower-mobility parallel manipulators with parallelogram joints. Using screw theory, the concept of twist graph is introduced and the twist graphs of two types of parallelogram joints are established in order to simplify the constraint analysis of the manipulators under study. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six Plu¨cker vectors of finite and infinite lines in the 3-dimensional projective space are reformulated in the superbracket in order to derive the geometric conditions for parallel singularities. The methodology is applied to three lower-mobility parallel manipulators with parallelogram joints: the Delta-linear robot, the Orthoglide robot and the H4 robot. The geometric interpretations of the singularities of these robots are given.

scholarly journals A transitive self-polar double-twenty of planes

1996 ◽  
Vol 61 (2) ◽  
pp. 249-257
Author(s):  
P. B. Kirkpatrick
Keyword(s):  
Projective Space ◽  
Dimensional Space ◽  
Involutory Automorphism ◽  
Square Roots ◽  
3 Dimensional ◽  
Unitary Polarity ◽  
Dimensional Projective Space

AbstractWe demonstrate the existence, in the 5-dimensional projective space over any field J in which 1 + 1 ≠ 0 and −1 is a square, of a non-degenerate double-twenty of planes (ℋ, K) with the property that there is a group of collineations which acts transitively on ℋ ∪ K while each element of the group either maps ℋ onto itself and K onto itself or else swaps ℋ with K. If there is an involutory automorphism of J which swaps the two square roots of −1, then (ℋ, K) is also self-polar (with respect to a unitary polarity). We describe some of the geometry (in both 5-dimensional and 3-dimensional space) associated with the double-twenty (ℋ, K) and its group.

scholarly journals Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space

2016 ◽  
Vol 73 ◽  
pp. 221-243 ◽  
Author(s):  
Xiaohong Jia ◽  
Wenping Wang ◽  
Yi-King Choi ◽  
Bernard Mourrain ◽  
Changhe Tu
Keyword(s):  
Projective Space ◽  
Intersection Curve ◽  
3 Dimensional ◽  
Dimensional Projective Space

scholarly journals A Characterization of the Hermitian Variety in Finite 3-Dimensional Projective Spaces

10.37236/3416 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Vito Napolitano
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Intersection Numbers ◽  
Combinatorial Characterization ◽  
Hermitian Variety ◽  
3 Dimensional ◽  
Dimensional Projective Space

A combinatorial characterization of a non-singular Hermitian variety of the finite 3-dimensional projective space via its intersection numbers with respect to lines and planes is given.   A corrigendum was added on March 29, 2019.

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