arXiv research

The paper classifies Killing tensor fields on Riemannian symmetric spaces.

Researchers found non-Killing tensor fields on certain symmetric spaces.

Characterizes Lorentzian manifolds with semi-symmetric metric connections.

A vector field on a Riemannian manifold is called conformal Killing if it generates one-parameter group of conformal transformations. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometri…

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…

Proves inequality for tensor fields on curved spaces.

The article recovers tensor fields from partial data using weighted divergent ray transforms.

Inverts rank m symmetric tensor fields using line integrals.

Systematic prolongation for Killing two-tensors in symmetric spaces.

A symmetric tensor field on a Riemannian manifold is called Killing field if the symmetric part of its covariant derivative is equal to zero. There is a one to one correspondence between Killing tensor fields and first integrals of the geodesic flow which depend polynomially on the velocity. Therefore Killing tensor fi…

We study left-invariant symmetric Killing 2-tensors on 2-step nilpotent Lie groups endowed with a left-invariant Riemannian metric, and construct genuine examples, which are not linear combinations of parallel tensors and symmetric products of Killing vector fields.

Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.

In this work, we show an injectivity result and support theorems for integral moments of a m-tensor field on a simple, real analytic, Riemannian manifold. Integral moments of m-tensor field were first introduced by Sharafutdinov. At first we generalize a Helgason type support theorem proven by Krishnan and Stefanov in …

The study finds points on surfaces where a tensor is conformal to a metric.

Stationary and axially symmetric space-times play an important role in astrophysics, particularly in the theory of neutron stars and black holes. The static vacuum sub-class of these space-times is known as Weyl's class, and contains the Schwarzschild space-time as its most prominent example. This paper is going to stu…

Characterizes symmetric Killing tensors on specific Lie groups.

Log Sobolev and Michael Simon inequalities for tensor fields on curved manifolds.

Quadratic Killing tensors on Lie groups are always decomposable.

New tensors help solve magnetic flow integrability.

New formula extracts full local information from ray transform data.

Proves inequalities for tensor fields on submanifolds using ABP method.

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

The paper characterizes integrability of tensors on manifolds.

The paper constructs a Poisson algebra bundle for multilocal observables.

We study in a uniform manner the properties of biconservative surfaces in arbitrary Riemannian manifolds. Biconservative surfaces being characterized by the vanishing of the divergence of a symmetric tensor field $S_2$ of type $(1,1)$, their properties will follow from general properties of a symmetric tensor field of …

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…

Generalizes Riemann's results on flat coordinates for non-symmetric bilinear forms.

Counterexample found to estimate for skew-symmetric tensors.

The study finds conditions for a third rank Killing tensor field on a 2D Riemannian torus.

New metric tensor field on symmetric matrices simplifies eigenvector computation.

We compute the eigenvalues with multiplicities of the Lichnerowicz Laplacian acting on the space of symmetric covariant tensor fields on the Euclidian sphere $S^n$. The spaces of symmetric eigentensors are explicitly given.

We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.

We compute the eigenvalues with multiplicities of the Lichnerowicz Laplacian acting on the space of complex symmetric covariant tensor fields on the complex projective space $P^n(\comp)$. The spaces of symmetric eigentensors are explicitly given.

In this note we discuss conditions under which a linear connection on a manifold equipped with both a symmetric (Riemannian) and a skew-symmetric (almost-symplectic or Poisson) tensor field will preserve both structures.

For a bounded N-dimensional domain with Lipschitz boundary we extend Korn's first inequality to incompatible tensor fields. For compatible tensor fields our estimate reduces to a non-standard variant of the well known Korn's first inequality. On the other hand, for skew-symmetric tensor fields our new estimate turns to…

We generalize reduction theorems for classical connections to operators with values in $k$-th order natural bundles. Using the first reduction theorem in order two we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.

Characterizes pseudo B-symmetric spacetimes and their implications in f(R) gravity.

Solves non-Abelian Rainich problem for SU(2) gauge fields.

We consider odd Poisson (odd symplectic) structure on supermanifolds induced by an odd symmetric rank $2$ (non-degenerate) contravariant tensor field. We describe the difference between odd Riemannian and odd symplectic structure in terms of the Cartan prolongation of the corresponding Lie algebras, and formulate an an…

Algebraic curvature tensors possess generators which can be formed from symmetric or alternating tensors S, A or tensors θwith an irreducible (2,1)-symmetry. In differential geometry examples of curvature formulas are known which contain generators on the basis of S or A realized by differentiable tensor fields in a na…

We consider generators of algebraic covariant derivative curvature tensors R' which can be constructed by a Young symmetrization of product tensors W*U or U*W, where W and U are covariant tensors of order 2 and 3. W is a symmetric or alternating tensor whereas U belongs to a class of the infinite set S of irreducible s…

New divergence identity for scalar curvature helps prove rigidity of tensors.

We consider complex projective space with its Fubini-Study metric and the X-ray transform defined by integration over its geodesics. We identify the kernel of this transform acting on symmetric tensor fields.

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…

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 …

We introduce an appropriate formalism in order to study conformal Killing (symmetric) tensors on Riemannian manifolds. We reprove in a simple way some known results in the field and obtain several new results, like the classification of conformal Killing $2$-tensors on Riemannian products of compact manifolds, Weitzenb…

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

We show that the symmetry classes of torsion-free covariant derivatives $\nabla T$ of r-times covariant tensor fields T can be characterized by Littlewood-Richardson products $σ[1]$ where $σ$ is a representation of the symmetric group $S_r$ which is connected with the symmetry class of T. If $σ= [λ]$ is irreducible the…