Control of Quadrotors Using the Hopf Fibration on SO(3)

2019 ◽  
pp. 199-215
Author(s):  
Michael Watterson ◽  
Vijay Kumar
Keyword(s):  
Hopf Fibration

scholarly journals The Hopf fibration over S8 admits no S1-subfibration

Topology ◽  
1992 ◽  
Vol 31 (2) ◽  
pp. 239-254 ◽  
Author(s):  
Bonaventure Loo ◽  
Alberto Verjovsky
Keyword(s):  
Hopf Fibration

scholarly journals Poisson Principal Bundles

2021 ◽  
Author(s):  
Shahn Majid ◽  
◽  
Liam Williams ◽  
Keyword(s):  
Quantum Group ◽  
Lie Group ◽  
Poisson Structure ◽  
Differential Calculus ◽  
Principal Bundle ◽  
Poisson Manifold ◽  
Spin Connection ◽  
Poisson Geometry ◽  
Hopf Fibration ◽  
Principal Bundles

We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space X is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the base has an inherited Poisson structure and Poisson-compatible contravariant connection. The latter are known to be the semiclassical data for a quantum differential calculus. The theory is illustrated by the Poisson level of the q-Hopf fibration on the standard q-sphere. We also construct the Poisson level of the spin connection on a principal bundle.

Yang-Mills Equations of General Connections and a Certain Solutions in the Quaternionic Hopf Fibration Over Four-Sphere

2021 ◽  
Vol 22 ◽  
pp. 121-135
Author(s):  
Kensaku Kitada
Keyword(s):  
Basic Equation ◽  
Hopf Fibration ◽  
Nontrivial Solutions ◽  
Yang Mills ◽  
Action Density ◽  
Usual Theory

We investigate a version of Yang-Mills theory by means of general connections. In order to deduce a basic equation, which we regard as a version of Yang-Mills equation, we construct a self-action density using the curvature of general connections. The most different point from the usual theory is that the solutions are given in pairs of two general connections. This enables us to get nontrivial solutions as general connections. Especially, in the quaternionic Hopf fibration over four-sphere, we demonstrate that there certainly exist nontrivial solutions, which are made by twisting the well-known BPST anti-instanton.

The geometry and topology of entanglement: Conifold, Segre variety, and Hopf fibration

2006 ◽  
Vol 6 (4&5) ◽  
pp. 400-409
Author(s):  
H. Heydari
Keyword(s):  
Higher Order ◽  
Segre Variety ◽  
Hopf Fibration ◽  
And Topology ◽  
Qubit States

We establish relations between conifold, Segre variety, Hopf fibration, and separable sets of pure two-qubit states. Moreover, we investigate the geometry and topology of separable sets of pure multi-qubit states based on the complex multi-projective Segre variety and higher order Hopf fibration. We show that the Segre variety and Hopf fibration give a unified geometrical and topological picture of multi-qubit states. We also construct entanglement monotones for multi-qubit states.

scholarly journals On the Hopf fibration S7 → S4 Over Z

1975 ◽  
Vol 59 ◽  
pp. 59-64 ◽  
Author(s):  
Takashi Ono
Keyword(s):  
Rational Numbers ◽  
Hopf Fibration ◽  
Quaternion Field

Let K be the classical quaternion field over the field Q of rational numbers with the quaternion units 1, i, j, k, with relations i2 = j2 = − 1, k = ij = −ji. For a quaternion x ∈ K, we write its conjugate, trace and norm by and Nx, respectively. Putand consider the map h: A → B defined by

scholarly journals Spin(9) geometry of the octonionic Hopf fibration

2013 ◽  
Vol 18 (3) ◽  
pp. 845-864 ◽  
Author(s):  
Liviu Ornea ◽  
Maurizio Parton ◽  
Paolo Piccinni ◽  
Victor Vuletescu
Keyword(s):  
Hopf Fibration

scholarly journals Stability and chaos in Kustaanheimo–Stiefel space induced by the Hopf fibration

2016 ◽  
Vol 459 (3) ◽  
pp. 2444-2454 ◽  
Author(s):  
Javier Roa ◽  
Hodei Urrutxua ◽  
Jesús Peláez
Keyword(s):  
Hopf Fibration

scholarly journals Algebraic links and the hopf fibration

Topology ◽  
1991 ◽  
Vol 30 (2) ◽  
pp. 259-265 ◽  
Author(s):  
Thomas Fiedler
Keyword(s):  
Hopf Fibration

First (fuzzy) Hopf map from irreps of SU(2)

Open Physics ◽  
2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Hossein Fakhri ◽  
Mehdi Lotfizadeh
Keyword(s):  
Vector Bundles ◽  
Hopf Fibration ◽  
Complex Vector ◽  
Spherical Basis ◽  
Hopf Map ◽  
One To One

AbstractUsing the spherical basis of the spin-ν operator, together with an appropriate normalized complex (2ν +1)-spinor on S 3 we obtain spin-ν representation of the U(1) Hopf fibration S 3 → S 2 as well as its associated fuzzy version. Also, to realize the first Hopf map via the spherical basis of the spin-1 operator with even winding numbers, we present an appropriate normalized complex three-spinor. We put the winding numbers in one-to-one correspondence with the monopole charges corresponding to different associated complex vector bundles.

Universal growth law for knot energy of Faddeev type in general dimensions

2008 ◽  
Vol 464 (2098) ◽  
pp. 2741-2757 ◽  
Author(s):  
Fanghua Lin ◽  
Yisong Yang
Keyword(s):  
Fine Structure ◽  
Field Configuration ◽  
Hopf Fibration ◽  
Essential Characteristic ◽  
Knot Energy

The presence of a fractional-exponent growth law relating knot energy and knot topology is known to be an essential characteristic for the existence of ‘ideal’ knots. In this paper, we show that the energy infimum E N stratified at the Hopf charge N of the knot energy of the Faddeev type induced from the Hopf fibration ( n ≥1) in general dimensions obeys the sharp fractional-exponent growth law , where the exponent p is universally rendered as , which is independent of the detailed fine structure of the knot energy but determined completely by the dimensions of the domain and range spaces of the field configuration maps.

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