The paper studies quarter-symmetric connections on Hermitian and Kähler manifolds.
problem Examining quarter-symmetric connections on almost Hermitian and Kähler manifolds.
method Analyzing the curvature tensors and their properties with respect to quarter-symmetric connections.
result Constructed tensors that do not depend on the quarter-symmetric connection generator, including the Weyl projective curvature tensor.
The paper studies para-Sasaki-like manifolds with a new metric connection.
problem Investigating new geometric structures on para-Sasaki-like manifolds.
method Deriving relations between connections, analyzing curvature tensors, studying solitons, constructing examples.
result Derived relations and properties of para-Sasaki-like manifolds with the generalized symmetric metric connection.
Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.
problem Exploring properties of second order symmetric parallel tensors in generalized f.pk-space forms.
method Analyzes the properties of second order symmetric parallel tensors and deduces the existence or non-existence of certain tensors and hypersurfaces.
result There does not exist second order skew-symmetric parallel tensor in f.pk-space form. There is no parallel hypersurface in a generalized f.pk-space form but there is semi-parallel hypersurface.
New neural networks respect symmetries in symmetric tensors, improving efficiency and generalization.
problem Learning from symmetric tensors efficiently and respecting their inherent symmetries.
method Developed two characterizations of linear permutation equivariant functions between symmetric power spaces of R^n.
result These functions are highly data efficient compared to standard MLPs and generalize well to different sizes of symmetric tensors.
The paper studies T-tensor of spherically symmetric Finsler metrics and characterizes metrics satisfying the T-condition.
problem Characterizing spherically symmetric Finsler metrics with vanishing T-tensor.
method Deriving a general expression for the T-tensor and characterizing metrics satisfying the T-condition.
result Characterization of spherically symmetric Finsler metrics with vanishing T-tensor.
The present study initially identify the generalized symmetric connections of type (α,β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α,β)=(1,0) and (α,β)=(0,1). Taking that into account, a ne…
The present study initially identified the generalized symmetric connections (α,β) typed, which can be regarded as more generalised forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively particularly when (α,β)=(1,0) and (α,β)=(0,1) are taken into con…
The paper studies a new connection on Riemannian manifolds and finds conditions for symplectic manifolds.
problem Exploring a new quarter-symmetric non-metric connection on Riemannian manifolds.
method Analyzes the properties and relations of the torsion tensor and curvature tensors of the new connection.
result Conditions for a manifold to be symplectic when endowed with the new connection.
New tensors help solve magnetic flow integrability.
problem Integrability of magnetic flows on specific manifolds.
method Introduced magnetic Killing symmetric tensors to construct first integrals.
result Proved integrability of invariant magnetic flows on 2-step nilmanifolds.
Characterizes Lorentzian manifolds with semi-symmetric metric connections.
problem Characterizing Lorentzian manifolds with specific metric connections.
method Analyzing semi-symmetric metric connections with vanishing curvature and recurrent torsion.
result Establishes conditions for perfect fluid and generalized Robertson-Walker spacetimes.
Researchers found non-Killing tensor fields on certain symmetric spaces.
problem Understanding Killing tensors on all Riemannian symmetric spaces.
method Constructed explicit examples of quadratic Killing tensors on quaternionic and Cayley projective spaces.
result Quadratic Killing tensors can be non-Killing on some symmetric spaces.
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…
The paper studies Stein-Weiss operators on symmetric tensors, extending previous work.
problem Understanding Stein-Weiss operators on symmetric tensors of arbitrary rank.
method Analyzing the decomposition of tensor spaces into irreducible components and computing Weitzenbock formulas.
result Unified framework for second-order Stein-Weiss operators and tools for geometric analysis.
Study on tautness tensor for Riemannian foliations.
problem Understanding tautness properties of Riemannian foliations.
method Investigating a symmetric 2-tensor related to mean curvature.
result Prove a tautness condition for compact manifolds.
Compatible tensors form a special Jordan algebra.
problem Understanding the algebraic structure of compatible tensors.
method Proving tensors form a Jordan algebra through symmetrized product properties.
result Riemann, Weyl, and curvature compatible tensors form a special Jordan algebra.
Systematic prolongation for Killing two-tensors in symmetric spaces.
problem Understanding Killing two-tensors in symmetric spaces.
method Systematic prolongation procedure for Killing two-tensors, focusing on locally symmetric spaces.
result Natural quadratic mapping from Killing fields to Killing two-tensors on irreducible locally symmetric spaces of compact type.
We introduce a new kind of Riemannian manifold that includes weakly-, pseudo- and pseudo projective- Ricci symmetric manifolds. The manifold is defined through a generalization of the so called Z tensor; it is named "weakly Z symmetric" and denoted by (WZS)_n. If the Z tensor is singular we give conditions for the exis…
We show that the space of algebraic covariant derivative curvature tensors R' is generated by Young symmetrized tensor products W*U or U*W, where W and U are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2),(3)}, {(2),(2 1)} or {(1 1)…
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…
Defines semi-symmetric metric connection on super warped products.
problem Computing curvature and Ricci tensors on super warped products.
method Introduced semi-symmetric metric connection and conditions for Einstein spaces.
result Conditions for super warped product spaces to be Einstein with semi-symmetric metric connection.
Paper proves existence of curves with specific geometric properties.
problem Existence of isometric immersions with prescribed second fundamental form.
method Introducing developments of curves with symmetric tensors and geometric construction.
result Existence of isometric immersions with prescribed second fundamental form.
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…
The paper classifies Killing tensor fields on Riemannian symmetric spaces.
problem Understanding Killing tensor fields on Riemannian symmetric spaces.
method Reduced study to compact irreducible spaces, introduced top slot Killing tensor fields, and classified quadratic fields.
result Quadratic Killing tensor fields on Riemannian symmetric spaces of rank one are spanned by top-slot and decomposable fields.
Upper bound found for divergence-free Killing 2-tensors on manifolds.
problem Bounding the space of divergence-free symmetric Killing 2-tensors.
method Witten deformation and Morse function analysis.
result Explicit calculation of dimension for p=2. Characterizes symmetric Killing tensors on specific Lie groups.
problem Understanding Killing tensors on specific Lie groups.
method Completely characterized left-invariant symmetric Killing tensors on almost abelian Lie groups.
result All such tensors are decomposable into polynomial expressions of Killing vector fields and metric.
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.
Proves inequality for tensor fields on curved spaces.
problem Generalizing inequality for tensor fields on curved spaces.
method Alexandrov-Bakelman-Pucci (ABP) method
result Proves Michael-Simon-Sobolev inequality for tensor fields.
The paper studies special warped products with a specific connection on super Riemannian manifolds.
problem Investigating curvature and Ricci tensors on super warped product spaces with a semi-symmetric non-metric connection.
method Defined a semi-symmetric non-metric connection, computed curvature and Ricci tensors, and introduced and analyzed two types of super warped product spaces.
result Conditions for two super warped product spaces with a semi-symmetric non-metric connection to be Einstein spaces are provided.
Estimates the probability of a random symmetric tensor being close to rank-one.
problem Estimating the probability of a random symmetric tensor being close to rank-one.
method Using Weyl's tube formula and techniques from Random Matrix theory, we study metric invariants of the real Veronese variety.
result Explicit formula for the reach and curvature coefficients of the real Veronese variety with respect to the Bombieri-Weyl metric.
Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with sections of the symmetric…
Sparse symmetric tensor regression reduces brain connectivity complexity.
problem Complex brain connectivity analysis in neuroimaging.
method Sparse symmetric tensor regression model for functional connectivity.
result Superior performance in Alzheimer's disease detection.
Formulae for non-symmetric connections derived from covariant derivatives.
problem Deriving commutation formulae for non-symmetric affine connections.
method Covariant derivatives of tensors with respect to symmetric and non-symmetric affine connections.
result Formulae for non-symmetric connections derived from covariant derivatives.
The paper proves Liouville-type theorems on Hadamard manifolds.
problem Non-existence of Killing-Yano tensors, Killing tensors, and harmonic symmetric tensors on Hadamard manifolds.
method Proofs use Liouville-type theorems on non-existence of subharmonic and harmonic functions on complete Riemannian manifolds, modified for Hadamard manifolds.
result Proves several Liouville-type theorems on Hadamard manifolds.
We consider generators of algebraic curvature tensors R which can be constructed by a Young symmetrization of product tensors U*w or w*U, where U and w are covariant tensors of order 3 and 1. We assume that U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2,1). …
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…
We consider equitorsion second type almost geodesic mappings of a non-symmetric affine connection space in this article. Using different computational methods, we obtained some invariants of these mappings. Last generalized Thomas projective parameter and Weyl projective tensor as invariants of a second type almost geo…
Study of symmetric affine surfaces with non-vanishing torsion.
problem Characterizing geometries of symmetric affine surfaces with torsion.
method Complete classification of local geometries assuming parallel torsion and local homogeneity for non-parallel torsion.
result Classification of local geometries for symmetric affine surfaces with torsion, generalizing previous results.
RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.
problem Lack of rotational symmetry in machine learning models for fluid systems.
method Introduces RotEqNet, a network that guarantees rotation-equivariance for high-order tensors.
result RotEqNet reduces errors and maintains rotation-equivariance in fluid systems.
On manifolds with an even Riemannian conformally compact Einstein metric, the resolvent of the Lichnerowicz Laplacian, acting on trace-free, divergence-free, symmetric 2-tensors is shown to have a meromorphic continuation to the complex plane, defining quantum resonances of this Laplacian. For higher rank symmetric ten…
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 paper analyzes tensor recovery from symmetric rank-one measurements using information theory.
problem Recovering tensors with low symmetric rank from symmetric rank-one measurements.
method Covering numbers argument, Carbery-Wright inequality, orthogonal polynomials, Fano's inequality.
result Near-optimal sample complexity bounds for log-concave distributions.
Tensor decomposition recovers Gaussian mixtures from moments.
problem Recovering Gaussian mixture models from datasets.
method Symmetric tensor decomposition of moment tensors built from empirical moments.
result Identifiable tensors with interpolation degree less than half their order.
A rank-n tensor on a Lorentzian manifold V whose contraction with n arbitrary causal future directed vectors is non-negative is said to have the dominant property. These tensors, up to sign, are called causal tensors, and we determine their general properties in dimension N. We prove that rank-2 tensors which map the n…
Characterizes pseudo B-symmetric spacetimes and their implications in f(R) gravity.
problem Characterizing pseudo B-symmetric spacetimes and their properties.
method Analyzes Codazzi type of B-tensor and applies f(R) gravity model.
result Pseudo B-symmetric spacetimes with Codazzi type B-tensor are conformally flat and Robertson-Walker spacetimes.
Equations link metrics with tensors, revealing curvature constraints.
problem Understanding curvature properties of geometric structures.
method Formal analogies to Einstein-Maxwell equations, studying Codazzi and conformal Killing equations.
result Constraints on scalar curvature of metrics in solutions.
Equivalence proven between uniformizing varieties and tensors, generalizing uniformization results.
problem Characterizing complex-projective varieties with klt singularities and ample canonical divisors.
method Constructing a uniformizing variation of Hodge structure from slope zero tensors and vice versa.
result Generalization of uniformization results to singular settings, including quotients of tube domains.
Study of equivariant Poisson 2-algebra bundles over configuration spaces.
problem Understanding Poisson structures on equivariant vector bundles over configuration spaces.
method Construction of induced-equivariance functor, Hadamard and Cauchy tensor products, symmetric 2-monoidal structure, free commutative 2-algebra, compatible Poisson bracket.
result Construction of free commutative 2-algebra and Poisson bracket on equivariant Poisson 2-algebra bundles.
We define a generalized mass for asymptotically flat manifolds using some higher order symmetric function of the curvature tensor. This mass is non-negative when the manifold is locally conformally flat and the σk curvature vanishes at infinity. In addition, with the above assumptions, if the mass is zero, then, nea…