Related papers: Torse-forming vector field with certain deformatio…
We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.
We consider shadowing properties for vector fields corresponding to different type of reparametrisations. We give an example of a vector field which has the oriented shadowing properties, but does not have the standard shadowing property.
In this paper, we give some properties of biharmonic hypersurface in Riemannian manifold has a torse-forming vector field.
We discuss the notions of indices of vector fields and 1-forms and their generalizations to singular varieties and varieties with actions of finite groups, as well as indices of collections of vector fields and 1-forms.
We classify, up to a natural equivalence relation, vector fields of the plane which belong to the kernel of a 1--form. This form can be closed, in which case the vector fields are integrable, or not, in which case the differential of the…
The vector field problem is an important and classical problem in differential topology. In this survey we shall consider the vector field problem focusing mainly on the class of compact homogeneous spaces.
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
We discuss different generalizations of the classical notion of the index of a singular point of a vector field to the case of vector fields or 1-forms on singular varieties, describe relations between them and formulae for their…
We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.
Vector field design on surfaces was originally motivated by applications in graphics such as texture synthesis and rendering. In this paper, we consider the idea of vector field design with a new motivation from computational topology. We…
Over a real field which is an extension of transcendence degree 1 of a hereditarily pythagorean base field, every quadratic form which is torsion decomposes into an orthogonal sum of 2-dimensional torsion forms. This is obtained from a more…
The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity. We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian…
Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…
In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…
In this paper, we give an explicit description of holomorphic polyvector fields on smooth compact toric varieties, which generalizes Demazure's result of holomorphic vector fields on toric varieties.
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize…
We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their…
Recently many methods have been proposed to create the vector fields, due to the academic interest and a variety of attractive applications such as for particle acceleration, optical trapping, particle manipulation, and fluorescence…