Related papers: Affine Hopf fibration
In this paper, we study the problem of finding the affine factorable surfaces in a 3-dimensional isotropic space with prescribed Gaussian (K) and mean (H) curvature. Because the absolute figure two different types of these surfaces appear…
In this letter we show numerical existence of O(4) Dirac-Born-Infeld (DBI) Textures living in (N +1) dimensional spacetime. These defects are characterized by $S^N\rightarrow S^3$ mapping, generalizing the well-known Hopf fibration into…
A new type of Hopf invariant is described for the fiber of the pinch map from the mapping cone of a map from A to X onto to the suspension of A; this is then used to study the boundary map in the fibration sequence of Cohen, Moore and…
We present a unifying framework for understanding several different versions of the Hopf fibration, and use this framework to reconcile two methods of representing rotations of 3-space by unitary matrices--the mathematician's convention…
We show that the natural S^1-bundle over a projective special Kaehler manifold carries the geometry of a proper affine hypersphere endowed with a Sasakian structure. The construction generalizes the geometry of the Hopf-fibration…
We consider the reductions of $2p$-dimensional particle system ($p=2,4,8$), associated with the Hopf map. For the third Hopf map we explicitly construct the functions associated to the symmetry related to the rotations in the fiber.
We give explicit formulas and asymptotics for the distribution of the index of the Brownian loop in the following geometrical settings: the complex projective line from which two points have been removed; the complex hyperbolic line from…
We prove a Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations, which improves a classical result by Crandall and Rabinowitz in the case where basic spaces are Hilbert spaces. Actually, our theorem does not need any…
Given any smooth fibration of the unit 3-sphere by great circles, we show that the distribution of 2-planes orthogonal to the great circle fibres is a tight contact structure, a fact well known in the special case of the Hopf fibrations.…
In this work we study the affine principal lines of surfaces in 3-space. We consider the binary differential equation of the affine curvature lines and obtain the topological models of these curves near the affine umbilic points (elliptic…
It is shown that analytic conformal submersions of $S^3$ are given by intersections of (not necessary closed) complex surfaces with a quadratic real hyper-surface in $\mathbb{C}P^3.$ A new description of the space of circles in the 3-sphere…
The paper presents applications of Toeplitz algebras in Noncommutative Geometry. As an example, a quantum Hopf fibration is given by gluing trivial U(1) bundles over quantum discs (or, synonymously, Toeplitz algebras) along their…
We study finite dimensional Hopf algebra actions on so-called filtered Artin-Schelter regular algebras of dimension n, particularly on those of dimension 2. The first Weyl algebra is an example of such on algebra with n=2, for instance.…
We study a class of affine manifolds equipped with a flat affine connection $\nabla$ and a global Riemannian metric $g$ that is diagonal in local affine coordinates. These structures are closely related to \emph{Hessian manifolds}, where…
The affine line minus one point is the underlying space of the algebraic torus of dimension one. However the fibration of an affine algebraic threefold by the affine line minus one point is not always the quotient morphism of the threefold…
We classify global surfaces of section for flows on 3-manifolds defining Seifert fibrations. We discuss branched coverings -- one way or the other -- between surfaces of section for the Hopf flow and those for any other Seifert fibration of…
For a finite group $G$, the Hurwitz space $\mathcal{H}^{in}_{r,g}(G)$ is the space of genus $g$ covers of the Riemann sphere with $r$ branch points and the monodromy group $G$. In this paper, we give a complete list of primitive genus one…
The purpose of this paper is to investigate finite-dimensional superbialgebras and Hopf superalgebras. We study connected superbialgebras and provide a classification of non-trivial superbialgebras and Hopf superalgebras in dimension $n$…
Building on the work of Nenciu we provide examples of non-factorizable ribbon Hopf algebras, and introduce a stronger notion of non-factorizability. These algebras are designed to provide invariants of $4$-dimensional $2$-handlebodies up to…
Given a Hopf fibration of a round sphere by parallel great subspheres, we prove that the projection map to the base space is, up to isometries of domain and range, the unique Lipschitz constant minimizer in its homotopy class. Similarly,…