scholarly journals Vector bundles on a three-dimensional neighborhood of a ruled surface

2005 ◽  
Vol 195 (1) ◽  
pp. 7-19 ◽  
Author(s):  
Edoardo Ballico ◽  
Elizabeth Gasparim
Keyword(s):  
Vector Bundles ◽  
Three Dimensional ◽  
Ruled Surface

scholarly journals Using Plücker Coordinates for Pumping Speed Evaluation of Molecular Pump in the DSMC Method

2001 ◽  
Vol 7 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Fong-Zhi Chen ◽  
Ming-June Tsai ◽  
Yu-Wen Chang ◽  
Rong-Yuan Jou ◽  
Hong-Ping Cheng
Keyword(s):  
Three Dimensional ◽  
Direct Simulation Monte Carlo ◽  
Flow Simulation ◽  
Vacuum Pump ◽  
Ruled Surface ◽  
Molecular Flow ◽  
Dsmc Method ◽  
Plücker Coordinates ◽  
Straight Line ◽  
Speed Performance

In this study, the Plücker coordinates representation is used to formulate the ruled surface and the molecular path for pumping speed performance evaluation of a molecular vacuum pump. The ruled surface represented by the Pliicker coordinates is used to develop a criterion for when gas molecules hit the pump surface wall. The criterion is applied to analyze the flow rate of a new developed vacuum pump in transition regimes by using the DSMC (Direct Simulation Monte Carlo) method. When a molecule flies in a neutral electrical field its path is a straight line. If the molecular path and the generators of a ruled surface are both represented by the Pliicker coordinates, the position of the molecular hit on the wall can be verified by the reciprocal condition of the lines. The Plücker coordinates representation is quite convenient in the DSMC method for this three-dimensional molecular flow simulation.

scholarly journals A Riemannian Geometry Theory of Three-Dimensional Binocular Visual Perception

Vision ◽  
2018 ◽  
Vol 2 (4) ◽  
pp. 43
Author(s):  
Peter Neilson ◽  
Megan Neilson ◽  
Robin Bye
Keyword(s):  
Riemannian Geometry ◽  
Vector Bundles ◽  
Three Dimensional ◽  
Geometric Theory ◽  
Visual Space ◽  
Human Movement ◽  
Image Features ◽  
Covariant Derivatives ◽  
Christoffel Symbols ◽  
Distance Relationship

We present a Riemannian geometry theory to examine the systematically warped geometry of perceived visual space attributable to the size–distance relationship of retinal images associated with the optics of the human eye. Starting with the notion of a vector field of retinal image features over cortical hypercolumns endowed with a metric compatible with that size–distance relationship, we use Riemannian geometry to construct a place-encoded theory of spatial representation within the human visual system. The theory draws on the concepts of geodesic spray fields, covariant derivatives, geodesics, Christoffel symbols, curvature tensors, vector bundles and fibre bundles to produce a neurally-feasible geometric theory of visuospatial memory. The characteristics of perceived 3D visual space are examined by means of a series of simulations around the egocentre. Perceptions of size and shape are elucidated by the geometry as are the removal of occlusions and the generation of 3D images of objects. Predictions of the theory are compared with experimental observations in the literature. We hold that the variety of reported geometries is accounted for by cognitive perturbations of the invariant physically-determined geometry derived here. When combined with previous description of the Riemannian geometry of human movement this work promises to account for the non-linear dynamical invertible visual-proprioceptive maps and selection of task-compatible movement synergies required for the planning and execution of visuomotor tasks.

scholarly journals Mannheim Offsets of Ruled Surfaces

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Keziban Orbay ◽  
Emin Kasap ◽  
İsmail Aydemir
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geodesic Curvature ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Arc Length ◽  
Spherical Indicatrix ◽  
Constant Distance ◽  
Mannheim Offset ◽  
Three Dimensional Space

In a recent works Liu and Wang (2008; 2007) study the Mannheim partner curves in the three dimensional space. In this paper, we extend the theory of the Mannheim curves to ruled surfaces and define two ruled surfaces which are offset in the sense of Mannheim. It is shown that, every developable ruled surface have a Mannheim offset if and only if an equation should be satisfied between the geodesic curvature and the arc-length of spherical indicatrix of it. Moreover, we obtain that the Mannheim offset of developable ruled surface is constant distance from it. Finally, examples are also given.

scholarly journals Ample vector bundles on a rational surface

1975 ◽  
Vol 59 ◽  
pp. 135-148 ◽  
Author(s):  
Toshio Hosoh
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Rational Surface ◽  
Ruled Surface ◽  
Necessary Condition ◽  
Abelian Surface ◽  
Closed Field ◽  
Stable Vector Bundle ◽  
Singular Curve ◽  
Rank 2

On a complete non-singular curve defined over the complex number field C, a stable vector bundle is ample if and only if its degree is positive [3]. On a surface, the notion of the H-stability was introduced by F. Takemoto [8] (see § 1). We have a simple numerical sufficient condition for an H-stable vector bundle on a surface S defined over C to be ample; let E be an H-stable vector bundle of rank 2 on S with Δ(E) = c1(E)2 - 4c2(E) ≧ 0, then E is ample if and only if c1(E) > 0 and c2(E) > 0, provided S is an abelian surface, a ruled surface or a hyper-elliptic surface [9]. But the assumption above concerning Δ(E) evidently seems too strong. In this paper, we restrict ourselves to the projective plane P2 and a rational ruled surface Σn defined over an algebraically closed field k of arbitrary characteristic. We shall prove a finer assertion than that of [9] for an H-stable vector bundle of rank 2 to be ample (Theorem 1 and Theorem 3). Examples show that our result is best possible though it is not a necessary condition (see Remark (1) §2).

scholarly journals Moduli spaces of vector bundles over ruled surfaces

1999 ◽  
Vol 154 ◽  
pp. 111-122 ◽  
Author(s):  
Marian Aprodu ◽  
Vasile Brînzănescu
Keyword(s):  
Line Bundle ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Ample Line Bundle ◽  
Sufficient Conditions ◽  
Ruled Surface ◽  
Stable Bundles ◽  
Isomorphism Classes ◽  
Numerical Invariants ◽  
Necessary And Sufficient

AbstractWe study moduli spaces M(c1, c2, d, r) of isomorphism classes of algebraic 2-vector bundles with fixed numerical invariants c1, c2, d, r over a ruled surface. These moduli spaces are independent of any ample line bundle on the surface. The main result gives necessary and sufficient conditions for the non-emptiness of the space M(c1, c2, d, r) and we apply this result to the moduli spaces ML(c1, c2) of stable bundles, where L is an ample line bundle on the ruled surface.

scholarly journals Moduli spaces of vector bundles on a singular rational ruled surface

2015 ◽  
Vol 180 (1) ◽  
pp. 399-413 ◽  
Author(s):  
Usha N. Bhosle ◽  
Indranil Biswas
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Ruled Surface

scholarly journals Singularities of Non-Developable Surfaces in Three-Dimensional Euclidean Space

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1106
Author(s):  
Jie Huang ◽  
Donghe Pei
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Singularity Theory ◽  
Structure Functions ◽  
Ruled Surface ◽  
Singular Points ◽  
Dimensional Euclidean Space ◽  
Smooth Curves ◽  
Developable Surfaces

We study the singularity on principal normal and binormal surfaces generated by smooth curves with singular points in the Euclidean 3-space. We discover the existence of singular points on such binormal surfaces and study these singularities by the method of singularity theory. By using structure functions, we can characterize the ruled surface generated by special curves.

scholarly journals Vector bundles over three-dimensional spherical space forms

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
Esdras Teixeira Costa ◽  
Oziride Manzoli Neto ◽  
Mauro Spreafico
Keyword(s):  
Vector Bundles ◽  
Three Dimensional ◽  
Spherical Space ◽  
Space Forms ◽  
3 Dimensional ◽  
Complete Answer ◽  
Spherical Space Forms ◽  
Low Dimensional

We consider the problem of enumerating theG-bundles over low-dimensional manifolds (dimension≤3) and in particular vector bundles over the three-dimensional spherical space forms. We give a complete answer to these questions and we give tables for the possible vector bundles over the 3-dimensional spherical space forms.

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