Related papers: Improving the Regularity of Vector Fields

Combining the Batchelor theorem and the Serre-Swan theorem, we come to that, given a smooth manifold $X$, a graded commutative $C^\infty(X)$-algebra $\cA$ is isomorphic to the structure ring of a graded manifold with a body $X$ iff it is…

Bonatti and da Luz have introduced the class of \emph{multi-singular hyperbolic} vector fields to characterize systems whose periodic orbits and singularities do not bifurcate under perturbation (called star vector fields). In this paper,…

We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of…

This article deals with the interpolating sesqui-harmonicity of a vector field $X$ viewed as a map from a Riemannian manifold $(M,g)$ to its tangent bundle $TM$ endowed with the Sasaki metric $g_{S}$. We show characterization theorem for…

We study almost Riemann solitons and almost Ricci solitons in an $(\alpha,\beta)$-contact metric manifold satisfying some Ricci symmetry conditions, treating the case when the potential vector field of the soliton is pointwise collinear…

Let $\rho_C$ be the regularity of the Hilbert function of a projective curve $C$ in $\mathbb P^n_K$ over an algebraically closed field $K$ and $\alpha_1,...,\alpha_{n-1}$ be minimal degrees for which there exists a complete intersection of…

I propose a notion of $(\omega_1,\beta)$-morass for the case $\omega_1 \leq \beta$.

A unit-vector field n on a convex three-dimensional polyhedron P is tangent if, on the faces of P, n is tangent to the faces. A homotopy classification of tangent unit-vector fields continuous away from the vertices of P is given. The…

We prove a multi-valued $C^{1,\alpha}$ regularity theorem for the varifolds in the class $\mathcal{S}_2$ (i.e., stable codimension one stationary integral $n$-varifolds admitting no triple junction classical singularities) which are…

Denote by $H_{pqm}$ the space of all planar $(p,q)$-quasihomogeneous vector fields of degree $m$ endowed with the coefficient topology. In this paper we characterize the set $\Omega_{pqm}$ of the vector fields in $H_{pqm}$ that are…

The classical results, initiated by Castelnuovo and Fano and later refined by Eisenbud and Harris, provide several upper bounds on the number of quadrics defining a nondegenerate projective variety. Recently, it has been revealed that these…

We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple…

On a Hermitian manifold we construct a symmetric $(1,1)$- tensor $H$ using the torsion and the curvature of the Chern connection. On a compact balanced Hermitian manifold we find necessary and sufficient conditions in terms of the tensor…

A global vector field $v$ on a "spacetime" differentiable manifold $\mathrm{V}$, of dimension $N+1$, defines a congruence of world lines: the maximal integral curves of $v$, or orbits. The associated global space $\mathrm{N}\_v$ is the set…

Let $(M^{n+1},g)$ be a closed Riemannian manifold, $n+1\geq 3$. We will prove that for all $m \in \mathbb{N}$, there exists $c^{*}(m)>0$, which depends on $g$, such that if $0<c<c^{*}(m)$, $(M,g)$ contains at least $m$ many closed $c$-CMC…

In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce an explicit formula for the the $S$-curvature of…

Let $(M,\omega)$ be an almost symplectic manifold ($\omega$ is a non degenerate, not closed, 2-form). We say that a vector field $X$ of $M$ is locally Hamiltonian if $L_X\omega=0,d(i(X)\omega)=0$, and it is Hamiltonian if, furthermore, the…

Fix a hyperelliptic curve $C/\mathbb{Q}$ of genus $g$, and consider the number fields $K/\mathbb{Q}$ generated by the algebraic points of $C$. In this paper, we study the number of such extensions with fixed degree $n$ and discriminant…

We investigate the open Closing Lemma problem for vector fields on the 2-dimensional torus. Under the assumption of bounded type rotation number, the $C^r$ Closing Lemma is verified for smooth vector fields that are area-preserving at all…

This paper investigates advanced notions of lineability and spaceability within the frameworks of sequence spaces and operator ideals. We propose the notion of \emph{Standard Sequence Classes} to provide an environment that unifies numerous…