Vorticity Gramian of compact Riemannian manifolds
General Mathematics
2022-10-14 v1
Abstract
The vorticity of a vector field on 3-dimensional Euclidean space is usually given by the curl of the vector field. In this paper, we extend this concept to n-dimensional compact and oriented Riemannian manifold. We analyse many properties of this operation. We prove that a vector field on a compact Riemannian manifold admits a unique Helmholtz decomposition and establish that every smooth vector field on an open neighbourhood of a compact Riemannian manifold admits a Stokes' type identity.
Keywords
Cite
@article{arxiv.2210.06552,
title = {Vorticity Gramian of compact Riemannian manifolds},
author = {Louis Omenyi and Emmanuel Nwaeze and Friday Oyakhire and Monday Ekhator},
journal= {arXiv preprint arXiv:2210.06552},
year = {2022}
}