arXiv research

SL(n) covariant valuations on Orlicz spaces are represented and characterized.

We prove the classification of the real vector subspaces of a quaternionic vector space by using a covariant functor which, to any pair formed of a quaternionic vector space and a real subspace, associates a coherent sheaf over the sphere.

We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static space-times with compact Riemannian parts.

The paper studies Finsler spaces with semi-concurrent vector fields and their equivalence to Riemannian spaces.

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

New pushforward operation on vector pseudo-bundles creates new examples.

The study classifies spaces with specific conformal vector fields.

Study of differential forms and vector fields on orbit spaces.

In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in view of root systems.

Paper introduces stratified vector bundles and their properties.

Study projective symmetries in Finsler spaces, showing reductions and constant flag curvature.

We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological vector spaces to Banach spaces.

Defines quaternionic k-vector fields on quaternionic Kähler manifolds.

This work describes compactifications of metric spaces and vector spaces using asymmetric norms.

Study Kähler geometry on vector bundles over elliptic curves.

The paper proves non-existence of torqued and anti-torqued vector fields on hyperbolic spaces.

Finite spaces can be or not coproducts of subspaces.

A study of proper affine vector fields in plane symmetric static space-times by using the rank of the Rieman matrix and holonomy. Studying proper affine vector fields in each case, It is shown that the special class of the above space-times admit proper affine vector fields.

Study Ricci vector fields on 2D space with diagonal metrics.

Maps vector fields between stacks and orbit spaces.

Novel metric space magnitude and weighting vectors improve machine learning tasks.

In this paper, we study geodesics and geodesic vectors for homogeneous exponential Finsler space and homogeneous infinite series Finsler space. Further, we find necessary and sufficient condition for a non-zero vector in these homogeneous spaces to be a geodesic vector.

Study vector fields and flows on singular spaces like submanifolds.

A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature vector if the mean curvature vector field H is parallel as a section of the normal bundle. Submanifolds with parallel mean curvature vector are important since they are critical points of some natural functionals. In this paper, we su…

New approach classifies conformal Killing vector fields for FLRW space-time.

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…

This research bridges Killing vectors and Lie algebras through induced vector fields.

We introduce G_2-vector fields, Rochesterian 1-forms and Rochesterian vector fields on manifolds with a closed G_2-structure as analogues of symplectic vector fields, Hamiltonian functions and Hamiltonian vector fields respectively, and we show that the spaces of G_2-vector fields and of Rochesterian vector fields are …

Defines cross product for m vectors in n-dimensional spaces.

Orbits of families of vector fields on a subcartesian space are shown to be smooth manifolds. This allows for a global description of a smooth geometric structure on a family of manifolds in terms of a single object defined on the corresponding family of vector fields. Stratified spaces, Poisson spaces and almost compl…

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…

In this paper, we characterize conformal vector fields of any (regular or singular) $(α,β)$-space with some PDEs. Further, we show some properties of conformal vector fields of a class of singular $(α,β)$-spaces satisfying certain geometric conditions.

Tensor approach simplifies Euclidean space descriptions.

Optimal rates for vector-valued regression on various norms.

We introduce coG_2-vector fields, coRochesterian 2-forms and coRochesterian vector fields on manifolds with a coclosed G_2-structure as a continuous of work from [15], and we show that the spaces of coG_2-vector fields and of coRochesterian vector fields are Lie subalgebras of the Lie algebra of vector fields with the …

Classifies vector field algebras in complex space.

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RK…

Study curvature lines of a vector field on surfaces.

Study on Kuranishi spaces of complex structures and vector bundles, showing isomorphisms and counterexamples.

The paper proves conditions for compact vacuum static spaces to be isometric to spheres.

New duality concept for vector spaces and groupoids.

We study the asymptotics of a family of link invariants on the orbits of a smooth volume-preserving ergodic vector field on a compact domain of the 3-space. These invariants, called linear saddle invariants, include many concordance invariants and generate an infinite-dimensional vector space of link invariants. In con…

The aim of the present paper is to investigate intrinsically the notion of a concircular $π$-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of a concurrent vector field in Finsler geometry. Some properties of concircular $π$-vector fie…

Study of generalized vector bundles and their geometric tools.

Study perturbations of submodules in Drury-Arveson space, finding smooth vector bundles with Hermitian connections.

In this paper, position vectors of a time-like curve with respect to standard frame of Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, we prove that position vector of every time-like space curve in Minkowski space E$^3_1$ satisfies a vector differential equation of fourth order. The general so…

In this paper, we prove that total space of every vector bundle with the base manifold on which the canonical isometric action acts freely, also carries a principal bundle structure. We also obtain another principal bundle based on the total space of given vector bundle.

The study characterizes helices in Euclidean and hyperbolic spaces.