相关论文: Parallel bundles in planar map geometries
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
Parametrized motion planning algorithms have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and form part of the input of the algorithm. In this paper we…
The general problem for consistency between arbitrary transports along paths in fibre bundles and bundle morphisms between them is formulated and investigated. The special case of one fibre bundle, its morphism and transport along paths…
We study geometric aspects of horizontal 2-plane distributions on the complement of the zero section in the 5-dimensional total space of a rank-3 vector bundle equipped with connection over a surface. We show that any surface in…
This paper studies properties of tilings of the plane by parallelograms. In particular it is established that in parallelogram tilings using a finite number of shapes all tiles occur in only finitely many orientations.
An analogue of the correspondence between GL(k)-conjugacy classes of matricial polynomials and line bundles is given for K-conjugacy classes, where K is one of the following: maximal parabolic, maximal torus, GL(k-1) embedded diagonally.…
In this note we give a complete description of all the hyperplane section of the projective bundle associated to the tangent bundle of $\mathbb{P}^2$ under its natural embedding in $\mathbb{P}^7.$ As an application one obtains a description…
Paravectors just like integers have a ring structure. By introducing an integrated product we get geometric properties which make paravectors similar to vectors. The concepts of parallelism, perpendicularity and the angle are conceptually…
In this paper, we investigate the structure of associated groups of symmetric quandles. Among other results, we explore the relationship between the associated group of a symmetric quandle and that of its underlying quandle. We provide a…
A geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying a metric connection with parallel skew-symmetric torsion. Besides the trivial case of the Levi-Civita connection, geometries with non-vanishing parallel…
In this article, the existence of Ulrich bundles on projective bundles $\mathbb P(E) \to X$ is discussed. In the case, that the base variety $X$ is a curve or surface, a close relationship between Ulrich bundles on $X$ and those on $\mathbb…
In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We classified…
We describe moduli spaces of logarithmic rank $2$ connections on elliptic curves with $n \geq 1$ poles and generic residues. In particular, we generalize a previous work by the first and second named authors. Our main approach is to analyze…
We extend several geometric quantization results to the setting of big line bundles. More precisely, we prove the asymptotic isometry property for the map that associates to a metric on a big line bundle the corresponding sup-norms on the…
The Centre Symmetry Set of a planar curve $M$ is the envelope of affine chords of $M$, i.e. the lines joining points on $M$ with parallel tangent lines. In this paper we study global geometrical properties of this set including the number…
In this document, we study the interaction between different geometric structures that can be defined as morphisms of sections of the generalized tangent bundle $\mathbb TM:= TM\oplus T^*M\to M$. In particular, we show the behaviour of…
There are several ways of a construction of a boundary of a symmetric space using pencils of geodesics: the Karpelevich boundary, the visibility boundary, the associahedral boundary, and the sea urchin. We give explicit descriptions of…
Topological defects, such as disclination lines in nematic liquid crystals, are fundamental to many physical systems and applications. In this work, we study the behavior of nematic disclinations in thin parallel-plate geometries with…
In the Teichm\"uller space of a hyperbolic surface of finite type, we construct geodesic lines for Thurston's asymmetric metric having the property that when they are traversed in the reverse direction, they are also geodesic lines (up to…