arXiv research

Defines quaternionic k-vector fields on quaternionic Kähler manifolds.

Study BV operators on holomorphic polyvector fields on toric varieties.

We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete situations.

New theory allows simultaneous block-diagonalization of commuting operator fields.

Study finds conditions for operator fields to be in strictly upper triangular form in small dimensions.

Novel duality theory for operator Frobenius algebras solves long-standing hydrodynamic integrable systems problem.

Solves problem of describing transformations for upper triangular Toeplitz operators.

We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a linear operator on the respected tangent space. Collectively, these operators form…

NON model improves tabular data classification accuracy.

Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.

The study introduces polarization of generalized Nijenhuis torsions and their relevance in operator fields.

Using holographic renormalization coupled with the Caffarelli/Silvestre\cite{caffarelli} extension theorem, we calculate the precise form of the boundary operator dual to a bulk scalar field rather than just its average value. We show that even in the presence of interactions in the bulk, the boundary operator dual to …

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called character…

Promotes spectral functionals to noncommutative fields and proves a theorem.

The article studies eigenvalues and spectrum of magnetic Dirac operators.

New Bol operators identified on superstrings.

It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such obstacle follows that manifold as pseudo-Riemannian manifold is locally non-reducible.…

This paper extends transfer operator theory to McKean-Vlasov equations.

Study approximates operators on labelled conditional distributions for non-exchangeable systems.

The paper proposes a method to sample quantum field configurations using neural operators and flows.

This paper presents two results conserning real hypersurfaces in CP^{2} and CH^{2}. More precisely, it is proved that real hypersurfaces equipped with structure Jacobi operator satisfying condition $\mathcal{L}_{X}l=\nabla_{X}l$, where \emph{X} is a vector field orthogonal to structure vector field $ξ$, do not exist. A…

We consider a magnetic Schrödinger operator $H^h$, depending on a semiclassical parameter $h>0$, on a compact Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the intensity of the magnetic field $b$ is strictly positive. We give a survey of the results on asympt…

Study Rarita-Schwinger fields on nearly Kähler manifolds, finding coinciding spaces of fields and deformations.

The study refines stability results for Yang-Mills fields and harmonic maps.

Extends elliptic operator regularity to maximally hypoelliptic operators.

Researchers describe local properties of Haantjes operators.

We apply the graph complex method to vector fields depending naturally on a set of vector fields and a linear symmetric connection. We characterize all possible systems of generators for such vector-field valued operators including the classical ones given by normal tensors and covariant derivatives. We also describe t…

Study linear differential operators on special manifolds.

Inverts rank m symmetric tensor fields using line integrals.

The article studies spinor and tensor fields on curved spaces, deriving formulas and spectra.

Computes indices of mixed order Dirac-type operators and related tensor fields.

The space of differential operators acting on skewsymmetric tensor fields or on smooth forms of a smooth manifold are representations of its Lie algebra of vector fields. We compute the first cohomology spaces of these representations and show how they are related to the cohomology with coefficients in ther space of sm…

Proves Hadamard states for Dirac fields on manifolds with timelike boundaries.

Let $M$ be a smooth manifold, $\cal S$ the space of polynomial on fibers functions on $T^*M$ (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space of the Lie algebra, $Vect(M)$, of vector fields on $M$ with coefficients in the space of linear differential operators on $\cal S$. This co…

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $α$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we cons…

New formula extracts full local information from ray transform data.

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for $CR$ manifolds and Hörmander's bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial diffe…

The paper finds manifolds with many Rarita-Schwinger fields.

We introduce a weighted de Rham operator which acts on arbitrary tensor fields by considering their structure as r-fold forms. We can thereby define associated superpotentials for all tensor fields in all dimensions and, from any of these superpotentials, we deduce in a straightforward and natural manner the existence …

Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.

We study steady-state magnetic fields in the geometric setting of positive curvature on subdomains of the three-dimensional sphere. By generalizing the Biot-Savart law to an integral operator BS acting on all vector fields, we show that electrodynamics in such a setting behaves rather similarly to Euclidean electrodyna…

A graph theory approach defines curl and decomposes vector fields.

We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.

The stability of the 3-dimensional Hopf vector field, as a harmonic section of the unit tangent bundle, is viewed from a number of different angles. The spectrum of the vertical Jacobi operator is computed, and compared with that of the Jacobi operator of the identity map on the 3-sphere. The variational behaviour of t…

In this paper we define and study the moduli space of metric-graph-flows in a manifold M. This is a space of smooth maps from a finite graph to M, which, when restricted to each edge, is a gradient flow line of a smooth (and generically Morse) function on M. Using the model of Gromov-Witten theory, with this moduli spa…

It is proved the non-existence of Hopf hypersurfaces in $G_{2}({\Bbb C}^{m+2})$, $m \geq 3$, whose normal Jacobi operator is semi-parallel, if the principal curvature of the Reeb vector field is non-vanishing and the component of the Reeb vector field in the maximal quaternionic subbundle ${\frak D}$ or its orthogonal …

New characterizations of ruled real hypersurfaces in complex projective space found.

Study geodesic ray transform on 2D manifolds with conjugate points.