Curvature tensors can always be matched to a metric tensor under certain conditions.
problem Sectionally positive curvature tensors and their relationship to metric tensors.
method Existence and uniqueness of a metric tensor gab such that Rabcdgbd=gacλ. result A metric tensor gab can be found for sectionally positive curvature tensors, and it is unique up to a constant factor. 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.
We construct a metrical framed structure on the tensor bundle of a Riemannian manifold equipped with a Cheeger-Gromoll type metric and by restricting this structure to the tensor sphere bundle, we obtain an almost metrical paracontact structure on the tensor sphere bundle. Moreover, we show that the tensor sphere bundl…
New concept of metric Lie algebras helps classify Lie groups.
problem Classifying Lie groups based on conformal Killing symmetric tensors.
method Introducing metric Lie algebras of Killing type and proving conditions for these algebras.
result Conditions for Lie algebras to be of Killing type with respect to any positive definite metric.
The paper constructs metrics on compact manifolds using Aubin's deformations.
problem Existence of metrics with non-vanishing Weyl tensor on compact manifolds.
method Special metric deformations introduced by Aubin.
result Existence of metrics with non-vanishing Weyl tensor on compact manifolds, no topological obstructions in dimension four.
A tensor field generates separation of variables for certain metrics.
problem Finding metrics with specific tensor field properties.
method Constructing differential invariants for a (1,1)-tensor field. result Explicit system of invariants for metrics generating separation of variables.
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.
The paper classifies tensors on specific Lorentzian metrics.
problem Classification of tensors on homogeneous plane waves.
method Framework of BGG operators to derive explicit formulae.
result Explicit formulae for irreducible Killing and conformal Killing 2-tensors identified.
Study characterizes Finsler metrics with first integrals using specific curvature tensors.
problem Characterizing Finsler metrics with first integrals.
method Used χ-curvature and mean Berwald curvature to characterize the metrics. result Characterized a class of Finsler metrics admitting first integrals.
The paper studies Kropina metrics with a specific curvature property.
problem Characterizing Kropina metrics with isotropic scalar curvature.
method Tensor analysis to derive expressions and characterize metrics.
result Characterization of Kropina metrics with isotropic scalar curvature.
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.
The paper classifies special types of contact metric manifolds with curvature conditions.
problem Classifying N(κ)-contact metric manifolds with specific curvature tensors. method Examining flatness conditions on T-curvature tensor and analyzing specific curvature tensors. result A classification of N(κ)-contact metric manifolds under various curvature conditions. In this paper, we study Randers metrics and find a condition on Ricci tensor of these metrics to be Berwaldian. This generalize Shen's Theorem which says: every R-°at complete Randers metric is locally Minkowskian. Then we find a necessary and sufficient condition on Ricci tensor under which a Randers metric of scalar …
Estimates metric tensor on neuromanifolds using Fisher information and random methods.
problem Computing the metric tensor on high-dimensional neuromanifolds efficiently and accurately.
method Deterministic bounds and unbiased random estimators based on Hutchinson's trace method.
result An efficient random estimator with bounded standard deviation.
The paper generalizes Riemann curvature for manifolds with discontinuous metrics.
problem Generalizing Riemann curvature for manifolds with discontinuous metrics.
method Proposes a generalized Riemann curvature tensor combining angle defects and jumps in second fundamental forms.
result The generalized curvature tensor approximates classical curvature for smooth approximations of metrics.
In this paper, we consider Randers change of some special (α,β)− metrics. First we find the fundamental metric tensor and Cartan tensor of these Randers changed (α,β)−metrics. Next, we establish a general formula for inverse of fundamental metric tensors of these metrics. Finally, we find the necessary and su…
The main purpose of this paper is to investigate the Schouten-Weyl tensor on the three-dimensional Lie groups with left-invariant Lorenzian metrics. The left-invariant Lorentzian metrics on the three-dimensional Lie groups with squared length zero Schouten-Weyl tensor are studied. Moreover, the three-dimensional metric…
Relates geodesic integrals to Killing tensors, exploring their dimensions.
problem Understanding geodesic integrals and Killing tensors in Riemannian geometry.
method Relating rational integrals of geodesic flow to relative Killing tensors, analyzing their span and dimensions.
result Upper bounds on dimensions of spaces spanned by these integrals and tensors.
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.
Study invariant CKY 2-forms on 5D Lie groups, classifying and determining their properties.
problem Classifying and understanding CKY 2-forms on 5D Lie groups.
method Classification and analysis of 5D metric Lie algebras with CKY tensors.
result First examples of CKY 2-forms on metric Lie algebras without Sasakian structures.
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.
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.
Enhances geodesic fiber tracking in white matter using modified metrics and tensor data.
problem Improving the accuracy and robustness of geodesic fiber tracking in white matter.
method Modification of geodesic ray-tracing method using rescaled metrics and fourth-order tensor data.
result More satisfactory results in the construction of white matter tracts as geodesics.
On a manifold with boundary, we deform the metric conformally. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in the interior, provided that there exists a subsolution.
Killing tensors on complex projective space are identified and generated by Killing fields.
problem Identifying Killing tensors on complex projective space.
method Determining Killing tensors of arbitrary rank on complex projective space with Fubini-Study metric.
result Complex projective spaces are generated by Killing fields.
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.
Using Hilbert's criterion, we consider the stress-energy tensor associated to the bienergy functional. We show that it derives from a variational problem on metrics and exhibit the peculiarity of dimension four. First, we use this tensor to construct new examples of biharmonic maps, then classify maps with vanishing or…
The paper proves geometric comparisons on metric measure spaces with integral Bakry-Émery Ricci tensor bounds.
problem Geometric comparisons on metric measure spaces with specific tensor bounds.
method Integral radial Bakry-Émery Ricci tensor bounds and potential function/gradient bounds.
result Diameter and eigenvalue estimates on smooth metric measure spaces.
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.
We define a Weyl-type curvature tensor that provides a characterisation for Finsler metrics of constant flag curvature. When the Finsler metric reduces to a Riemannian metric, the Weyl-type curvature tensor reduces to the classic projective Weyl tensor. In the general case, the Weyl-type curvature tensor differs from t…
In this article, we examine the behavior of the Riemannian and Hermitian curvature tensors of a Hermitian metric, when one of the curvature tensors obeys all the symmetry conditions of the curvature tensor of a Kähler metric. We will call such metrics G-Kähler-like or Kähler-like, for lack of better terminologies. Such…
The aim of this note is to study the measure-valued Ricci tensor on smooth metric measure space with boundary, which is a generalization of Bakry-Emery's modified Ricci tensor on weighted Riemannian manifold. As an application, we offer a new approach to study curvature-dimension condition of smooth metric measure spac…
Researchers solve metric curvature equations on manifolds with boundary.
problem Finding complete conformal metrics with specific curvature functions.
method Revealed algebraic structure of fully nonlinear equations; used topological obstructions.
result Solved a class of fully nonlinear equations for conformal metrics.
Paper solves tensor problem for holomorphic vector bundles.
problem Existence of Hermitian metrics with prescribed Hermitian-Yang-Mills tensors.
method New comparison theorem for Hermitian-Yang-Mills tensors.
result Existence of unique smooth Hermitian metric for any positive-definite tensor.
Study on 3D Lie groups finds all generalized Einstein metrics.
problem Classifying generalized Einstein metrics on 3D Lie groups.
method Developed theory of left-invariant generalized pseudo-Riemannian metrics, computed Ricci tensor, determined all metrics.
result Determined all generalized Einstein metrics on three-dimensional Lie groups.
The curvature properties of Robinson-Trautman metric have been investigated. It is shown that Robinson-Trautman metric admits several kinds of pseudosymmetric type structures such as Weyl pseudosymmetric, Ricci pseudosymmetric, pseudosymmetric Weyl conformal curvature tensor etc. Also it is shown that the difference $R…
We refine a metric bunching estimate for pinched manifolds.
problem Improving an unstable bunching estimate for pinched metrics.
method Compact Riemannian manifolds with pointwise negatively pinched curvature tensor.
result Improved unstable bunching estimate.
Study on generalized quasi-Einstein structures in contact geometry.
problem Characterizing and understanding generalized quasi-Einstein structures in contact geometry.
method Investigation of properties, existence, and characterizations of generalized quasi-Einstein normal metric contact pair manifolds.
result Normal metric contact pair manifolds with generalized quasi-constant curvature are generalized quasi-Einstein manifolds.
This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with 1-dimensional fibre. For this, we have considered a Melvin type static, cylindrically symmetric spacetime metric in Weyl form and it is found that such metric, in gen…
Study Codazzi tensors in space-times, linking to Cotton gravity.
problem Understanding Codazzi tensors and their role in space-times.
method Analyzing geometric properties and proving conditions for Codazzi tensors.
result Codazzi tensors restrict space-times, influencing energy-momentum tensors in Cotton gravity.
Local fractional derivatives affect Riemann curvature tensor to zero.
problem Investigating how local fractional derivatives influence the Riemann curvature tensor.
method Introduced a general local fractional derivative operator and defined a specific Riemannian metric tensor field.
result The Riemann curvature tensor of the new metric is identically zero, indicating local isometry to Euclidean space.
On 5-dimensional almost contact B-metric manifolds, the form of any Kähler-type tensor (i.e. a tensor satisfying the properties of the curvature tensor of the Levi-Civita connection in the special class of the parallel structures on the manifold) is determined. The associated 1-forms are derived by the scalar curvature…
Solves modified Schouten tensor problems in conformal metric classes.
problem Prescribed problems for modified Schouten tensors in conformal classes of metrics.
method Uniform ellipticity confirmation under topological and functional constraints.
result Extends results from previous work on smooth complete metrics.
Survey on manifolds satisfying generalized Einstein conditions.
problem Characterizing semi-Riemannian manifolds under specific curvature conditions.
method Analyzing the difference tensor R.C-C.R expressed as linear combinations of Tachibana tensors.
result Recent results on manifolds and submanifolds satisfying generalized Einstein conditions.
Study shows no hidden symmetries in specific spacetime metrics.
problem Demonstrating the absence of Killing tensors in Koutras-McIntosh spacetimes.
method Geometric theory of overdetermined PDEs and Cartan prolongation-projection method.
result No Killing tensors of low degrees in Wils metrics and generic pp-waves.
The paper solves a problem related to Higgs bundles and Hermitian metrics.
problem Existence of Hermitian metrics with prescribed Hermitian-Yang-Mills tensors for Higgs bundles.
method Solving the prescribed Hermitian-Yang-Mills tensor problem for Higgs bundles over compact complex manifolds.
result For any Hermitian positive definite tensor, there exists a unique smooth Hermitian metric on the Higgs bundle.
The study finds points on surfaces where a tensor is conformal to a metric.
problem Existence of conformal points on surfaces.
method Analyzes symmetric bilinear two-tensor fields and Riemannian metrics.
result Provides conditions for the existence of conformal points.
We descrive examples of metrics in the conformal class [g] on complete conformally flat Riemannian manifolds (M,g]. These metrics have a constant scalar curvature and an harmonic curvature with non parallel Ricci tensor.