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<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7634_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb{R}}^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> is given. Operators of this class are invariant with respect to translations of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7634_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb{R}}^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> and are transformed by the covariant way under rotations of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7634_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb{R}}^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>.</p>

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First-Order Covariant Differential Operators

  • 期刊论文

  • 发表日期：

    2025年2月26日

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  • Yu. P. Virchenko,
  • A. V. Subbotin

摘要

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 \({\mathbb{R}}^{3}\) R 3 is given. Operators of this class are invariant with respect to translations of \({\mathbb{R}}^{3}\) R 3 and are transformed by the covariant way under rotations of \({\mathbb{R}}^{3}\) R 3 .