Vorticity Gramian of compact Riemannian manifolds

Louis Omenyi; Emmanuel Nwaeze; Friday Oyakhire; Monday Ekhator

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arXiv · 2210.06552

Vorticity Gramian of compact Riemannian manifolds

Louis Omenyi·Emmanuel Nwaeze·Friday Oyakhire·Monday Ekhator

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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.

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Louis Omenyi, Emmanuel Nwaeze, Friday Oyakhire, Monday Ekhator. 2022-09-17. Vorticity Gramian of compact Riemannian manifolds. https://arxiv.org/abs/2210.06552

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