An algorithm is given for bringing the equations of monomial first integrals of arbitrary degree of the geodesic motion in a Riemannian space Vn into the form (FA) k = ∑ B ΓkABFB . The FA are the components of a Killing tensor Ki1...ir of arbitrary rank r and its symmetrized covariant derivatives. Explicit formulas are given for rank 1,2 and 3. Killing tensor equations in structural form allow ...

In their original formulation of the method of isotropic extension via structural tensors, which is meant for applications to the derivation of coordinate-free representation formulas for anisotropic constitutive functions, both Boehler and Liu start with the assumption that the invariance group of structural tensors is the symmetry group that defines the anisotropy of the constitutive function...

In this work we introduce the Killing-Yano symmetry on the phase space and we investigate the symplectic structure on the space of Killing-Yano tensors. We perform the detailed analyze of the ndimensional flat space and the Riemaniann manifolds with constant scalar curvature. We investigate the form of some multipole tensors, which arise in the expansion of a system of charges and currents, in ...

We construct the tensor hierarchies of generic, bosonic, 5and 6-dimensional field theories. The construction of the tensor hierarchy starts with the introduction of two tensors: the embedding tensor θ which tells us which vector is used for gauging and another tensor Z which tells us which vector is eaten by a 2-form. In dimensions d ≥ 5 these two (deformation) tensors are in principle unrelate...

In the recent application of scientific modeling, machine learning models are largely applied to facilitate computational simulations fluid systems. Rotation symmetry is a general property for most symmetric However, in general, current methods have no theoretical guarantee symmetry. By observing an important contraction and rotation operation on high order tensors, we prove that preserved via ...