Related papers: Torse-forming vector field with certain deformatio…
We discuss various old and new definitions of the notion of a vector field on a convenient manifold that can be proved to give rise to Lie algebras, and are in finite dimensions equivalent to the standard notion of a vector field.
We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically…
This note proposes a new notion of a gradient-like vector field and discusses its implications for the theory of Stein and Weinstein structures.
We develop a formalism of poly-vector deformations for Type IIB backgrounds with a block diagonal metric and non-vanishing self-dual 5-form RR field strength. Making use of the embedding of the Type IIB theory into the $\mathrm{E}_{6(6)}$…
These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differs slightly from…
We present the general theory of curves in conformal geometry using tractor calculus. This primarily involves a tractorial determination of distinguished parametrizations and relative and absolute conformal invariants of generic curves. The…
Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented.
A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…
We describe the deformation space of a solid torus with boundary modelled on convex ideal hyperbolic polyhedra. This deformation space is given by natural Gauss--Bonnet type inequalities on the dihedral angles. The result extends to solid…
It is known that $C^r$ Morse-Smale vector fields form an open dense subset in the space of vector fields on orientable closed surfaces and are structurally stable for any $r \in \mathbb{Z}_{>0}$. In particular, $C^r$ Morse vector fields…
We consider the category of perverse sheaves on a complex vector space smooth with respect to a stratification given by an arrangement of hyperplanes with real equations. As shown in an earlier wotk of two of the authors, this category can…
Physical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or…
Recently proposed forms for gauge transformations with finite parameters in double field theory are discussed and problematic issues are identified. A new form for finite gauge transformations is derived that reveals the underlying gerbe…
Smooth vector fields on $\mathbb{R}^n$ can be decomposed into the sum of a gradient vector field and divergence-free (solenoidal) vector field under suitable hypotheses. This is called the Helmholtz-Hodge decomposition (HHD), which has been…
We propose a novel matrix regularization for tensor fields. In this regularization, tensor fields are described as rectangular matrices and both area-preserving diffeomorphisms and local rotations of the orthonormal frame are realized as…
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…
Transverse deflecting cavities are used for a number of applications in modern accelerators. In this paper we discuss the fields of these cavities, some of their applications, and some important aspects of their design.
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
$G$-deformability of maps into projective space is characterised by the existence of certain Lie algebra valued 1-forms. This characterisation gives a unified way to obtain well known results regarding deformability in different geometries.
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical…