相关论文: Hessian Tensor and Standard Static Space-times
We study the spectrum $\{\lambda_j(m)\}_{j=1}^{\infty}$ of a timelike Killing vector field $Z$ acting as a differential operator $D_Z$ on the Hilbert space of solutions of the massive Klein-Gordon equation $(\Box_g + m^2) u = 0$ on a…
We study the wave function of a tensor model in the canonical formalism by Hamiltonian Monte Carlo method for Lie group symmetric or nearby values for the argument of the wave function, and show that there emerge Lie-group symmetric…
We study geometric properties of a random Gaussian short-time correlated velocity field by considering statistics of a passively advected metric tensor. That describes universal properties of fluctuations of tensor objects frozen into the…
The main purpose of the paper is to investigate Killing vector field on the tangent bundle T(M_{n}) of the Riemannian manifold with respect to the Levi-Civita connection of the metric II+III .
When spacetime torsion is present, geodesics and autoparallels generically do not coincide. In this work, the well-known method that uses Killing vectors to solve the geodesic equations is generalized for autoparallels. The main definition…
The supersymmetric extension of charged point particle's motion is applied to investigate symmetries of gravitational fields and electromagnetic fields. We mainly focus on the role of the Killing- Yano tensors of both usual and generalized…
The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a…
In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the…
The difference tensor R.C-C.R of a semi-Riemannian manifold (M,g), dim M > 3, formed by its Riemannian-Christoffel curvature tensor R and the Weyl conformal curvature tensor C, under some assumptions, can be expressed as a linear…
In this paper, we study generalized $m$-quasi-Einstein $(M^n,g,X,\lambda)$ under natural conditions on the potential vector field. We show that, under suitable integral assumptions, the potential vector field is Killing, extending earlier…
Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such…
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…
In this paper we continue the study of bi-conformal vector fields started in {\em Class. Quantum Grav.} {\bf 21} 2153-2177. These are vector fields defined on a pseudo-Riemannian manifold by the differential conditions $\lie P_{ab}=\phi…
The antiferromagnetic Heisenberg Hamiltonian is investigated on a truncated tetrahedron, which is a closed 12 site system. We find that the ground state has many similarities to that of $C_{60}$. We study 2- and 4-spin correlations in the…
In all $n(\ge 3)$-dimensional gravitation theories whose Lagrangians are functions of the Riemann tensor and metric, we show that static solutions are absent unless the total energy-momentum tensor for matter fields is of type I in the…
New geometries were obtained by adding a suitable surface term involving the components of the angular momentum to the corresponding free Lagrangians. Killing vectors, Killing-Yano and Killing tensors of the obtained manifolds were…
We determine the space of commuting symmetries of the Laplace operator on pseudo-Riemannian manifolds of constant curvature, and derive its algebra structure. Our construction is based on the Riemannian tractor calculus, allowing to…
Deriving the motion of a compact mass or charge can be complicated by the presence of large self-fields. Simplifications are known to arise when these fields are split into two parts in the so-called Detweiler-Whiting decomposition. One…
In recent papers [1-3], we have discussed matter symmetries of non-static spherically symmetric spacetimes, static plane symmetric spacetimes and cylindrically symmetric static spacetimes. These have been classified for both cases when the…
We discuss the covariant formulation of the dynamics of particles with abelian and non-abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of…