First-order covariant differential operators

Yu. P. Virchenko ; A. V. Subbotin

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 187 (2020), pp. 19-30.

Résumé

An internal description of the class of all nonlinear differential operators of the first order on the space of collections consisting of continuously differentiable vector and scalar fields on $\mathbb{R}^3$ is given. Operators of this class are invariant with respect to translations of $\mathbb{R}^3$ and are transformed by the covariant way under rotations of $\mathbb{R}^3$.

Détail

Keywords: first-order differential operator, divergence differential operator, vector field, pseudo-vector field, covariance.

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