arXiv research

Holographic reconstruction over local fields using Radon transform.

Derives localization formulas in Batalin-Vilkovisky formalism.

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 present an algebraic procedure that finds the Lie algebra of the local Killing fields of a smooth metric. In particular, we determine the number of independent local Killing fields about a given point on the manifold. Spaces of constant curvature and locally symmetric spaces are also discussed. Furthermore, we obtai…

Defines vector fields and differential forms on local C-infinity-ringed spaces.

Zermelo deformation preserves geodesics and curvature in Finsler metrics.

LSNN improves CNN by smoothing local receptive fields.

In this paper, it is proved that any conformal vector field is homothetic on a locally projectively flat $(α,β)$-space of non-Randers type in dimension $n\ge 3$, and the local solutions of such a vector field are determined. While on a locally projectively flat Randers space, examples showthat the conformal vector fiel…

New method constructs axial vector fields and defines quasi-local spin-angular momentum.

New approach to Lagrangian field theories using pro-finite structures and L-infinity algebras.

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

Characterizes and describes selfsimilar Hessian manifolds with homothetic vector fields.

Compute local cohomology of vector fields on manifolds.

Compact lcK manifolds with holomorphic Lee field are Vaisman under certain conditions.

Researchers found 5 local fields to uniquely describe 3D director fields, related through 6 differential relations.

Local Lorentzian theorem preserves metrics or makes them flat.

Local invertibility of higher rank tensor fields on curved manifolds proven.

An explicit model of fiber bundle with local fibers being disinct copies of vector 3-space is introduced. They are endowed with frames which are used as local isotopic ones. The field local of isotopic frames is considered as gauge field itself while the form of gauge connections is derived from it. A covariant equatio…

We give a full geometrical description of local totally geodesic unit vector field on Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its unit tangent bundle with the Sasaki metric.

We define two types of local indices of a vector field at an isolated zero on the boundary, and prove Poincare-Hopf-type index theorems for certain vector fields on a compact smooth manifold which have only isolated zeros.

In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(α,β)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to study conformal vector fields of some classes of $(α,β)$ spaces under certain c…

The paper proves a Basmajian identity for non-Archimedean local fields.

Local description of solvable Lie algebras of vector fields.

Generalizing local Gromov-Witten theory, in this paper we define a local version of symplectic field theory. When the symplectic manifold with cylindrical ends is four-dimensional and the underlying simple curve is regular by automatic transversality, we establish a transversality result for all its multiple covers and…

Using the navigation data (h,W) of a Kropina space, we characterize weakly-Berwald Kropina spaces and Berwald Kropina spaces by means of the Killing vector field W and the parallel vector field W, respectively. Moreover, the local 1-parameter group of Finslerian local isometries of the Kropina space coincides with the …

We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and th…

Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.

Study vector fields with complex singularities, proving bounds and formulas.

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.

Holomorphic residue formula for complex supermanifolds.

Paper presents a new Wi-Fi RSS and geomagnetic field database for indoor localization and trajectory estimation.

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 case. This is done using geometric methods, and studying local dynamics of seque…

Proves an analytical analogue of Morse's lemma for gradient fields near critical points.

Some observations about the local and global generality of gradient Kahler Ricci solitons are made, including the existence of a canonically associated holomorphic volume form and vector field, the local generality of solutions with a prescribed holomorphic volume form and vector field, and the existence of Poincare co…

We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.

Following the analogies between 3-dimensional topology and number theory, we study an idèlic form of class field theory for 3-manifolds. For a certain set $\mathcal{K}$ of knots in a 3-manifold $M$, we first present a local theory for each knot in $\mathcal{K}$, which is analogous to local class field theory, and then,…

In this paper we prove local analytic hypoellipticity for a degenerate sum of squares of complex vector fields generalizing those of Kohn in "Hypoellipticity and Loss of Derivatives". Kohn's article is to appear in the Annals of Mathematics with an appendix by Derridj and Tartakoff proving local analyticity in that cas…

We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed. Special attention is paid to the case of mappings between topological vector spaces ov…

Study examines Wang-Yau quasi-local energy in strong fields near apparent horizons.

Conformal vector fields on LCP manifolds are orthogonal and Killing.

Develops a new exponential map for time-varying vector fields.

Builds geometric structures for algebraic groups over real closed fields.

Two proofs of Kalman Theorem using flows of vector fields.

Paper compares algebraic quantum field theories and factorization algebras on Lorentzian manifolds.

New proof shows all conformal vector fields on complex hyperbolic space are Killing.

We review the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of Lagrange and Finsler geometry and higher dimension (Kaluza--Klein type) spaces. The problem of definition of spinors on gen…

The paper proves properties of Brauer equivalent number fields and applies them to geometric spaces.

Efficiently visualizes uncertainty in local divergence of 2D vector fields.