The value of the work done by an isotropic vector force field along an isotropic curve

Abstract

In the present paper we consider a 3-dimensional differentiable manifold $M$ equipped with a Riemannian metric $g$ and an endomorphism $Q$, whose third power is the identity and $Q$ acts as an isometry on $g$. Both structures $g$ and $Q$ determine an associated metric $f$ on $(M,g,Q)$. The metric $f$ is necessary indefinite and it defines isotropic vectors in the tangent space $T_{p}M$ at an arbitrary point $p$ on $M$. The physical forces are represented by vector fields. We investigate physical forces whose vectors are in $T_{p}M$ on $(M,g,Q)$. Moreover, these vectors are isotropic and they act along isotropic curves. We study the physical work done by such forces.

6 pages, Reported on International Scientific Conference "Tehsys 2020" -- Engineering, Technologies and Systems, Technical University of Sofia, Plovdiv Branch 14-16 May 2020