Vorticity Gramian of Compact Riemannian Manifolds
DOI:
https://doi.org/10.26713/cma.v13i2.1719Keywords:
Manifold, Curl, Metric tensor flow, Hodge star operator, Helmholtz decompositionAbstract
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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