arXiv research

The paper establishes a connection between force-free fields and conformally geodesic fields.

The Giroux correspondence and the notion of a near force-free magnetic field are used to topologically characterize near force-free magnetic fields which describe a variety of physical processes, including plasma equilibrium. As a byproduct, the topological characterization of force-free magnetic fields associated with…

A 3-dimensional vector field $B$ is said to be Beltrami vector field (force free-magnetic vector field in physics), if $B\times(\nabla\times B)=0$. Motivated by our investigations on projective an polynomial superflows, and as an important side result, in the first paper on this topic we constructed two unique Beltrami…

This is a postprint of our paper "Force free Moebius motions of the circle" (J. Geom. Symmetry Phys. 27 (2012) 59-65), which we hadn't uploaded to arXiv previously. We would like to draw attention to the relationship with the article "A geometry where everything is better than nice", by Larry Bates and Peter Gibson (to…

One considers a special class of PDEs systems and one determines the associated symmetry group. Particulary, for the Blair system, one finds the symmetry group. A solutions of the Blair system gives a conformally flat contact metric structure and also it defines a "force-free" model of solar physics. By using the symme…

The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional, and, as such, it is naturally identified with the boundary renor…

Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…

Study nonrigid dynamics of unitary groups on Lie groups via kinetic energy metrics.

Braided vector fields on spatial subdomains homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the vector field's topology -- the entanglement of its field lines -- is non-trivial,…

Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.

The paper explores how fields in higher dimensions are quantized.

Paper transforms torse-forming vector fields into simpler forms.

Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.

Conformal vector fields on LCP manifolds are orthogonal and Killing.

Paper describes holomorphic polyvector fields on toric varieties.

Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.

The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.

We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. In particular, in the case of admissible regular sheaves of local fields defined on a simply connected manifold, we obtain a global extension result for every local field of the sheaf. This generalizes…

We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz e…

Vector fields invariant under Lie group action are finitely generated by polynomial fields.

Quantum field theory uses Lorentzian bordisms to describe time evolution.

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold $M$. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …

Study on vector fields on Lie groups reveals surprising algebraic coincidences.

This work discovers latent field effects governing interacting dynamical systems.

Study proves conformal vector fields on certain Finsler manifolds are Killing fields.

For a submanifold M in a Euclidean space, the tangential component x^T of the position vector field x of M is the most natural vector field tangent to the Euclidean submanifold, called the canonical vector field of M. In this article, first we prove that the canonical vector field of every Euclidean submanifold is alwa…

Study magnetic field evolution in inhomogeneous axion stars.

In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the action principle to define the conservation law for such general fields. By con…

A Ricci soliton $(M,g,v,λ)$ on a Riemannian manifold $(M,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were studied recently in \cite{CD2}. The most important concurrent vector field is …

Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.

New field invariant refines real spectrum and relates to absolute Galois group.

Study biharmonic vector fields and unit vector fields on Riemannian manifolds.

Classifies vector fields in the kernel of a 1-form, up to equivalence.

Semisimple 4D field theories can't distinguish smooth 4-manifolds.

Stable knots and links can exist in electromagnetic fields.

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth famil…

Defines quaternionic k-vector fields on quaternionic Kähler manifolds.

Using a supergeometric interpretation of field functionals developed in previous papers, we show that for quite a large class of systems of nonlinear field equations with anticommuting fields, infinite-dimensional supermanifolds (smf) of classical solutions can be constructed. Such systems arise in classical field mode…

The paper classifies Killing tensor fields on Riemannian symmetric spaces.

Paper adds Fisher Information to mean field optimization for faster convergence.

A vector field on a Riemannian manifold is called conformal Killing if it generates one-parameter group of conformal transformations. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometri…

Enhances Hamiltonian systems stability through generalized double bracket vector fields.

A vector field s on a Riemannian manifold M is said to be harmonic if there exists a member of a 2-parameter family of generalised Cheeger-Gromoll metrics on TM with respect to which s is a harmonic section. If M is a simply-connected non-flat space form other than the 2-sphere, examples are obtained of conformal vecto…

Non-vanishing steady Euler flows and Beltrami fields found in high dimensions.

Study on generalized derivations in polynomial vector fields Lie algebras.

Generic singularities of line fields have been studied for lines of principal curvature of embedded surfaces. In this paper we propose an approach to classify generic singularities of general line fields on 2D manifolds. The idea is to identify line fields as bisectors of pairs of vector fields on the manifold, with re…

Lectures on topological field theories and differential cohomology.

Study on Einstein solitons with specific vector fields and their properties.