Abstract <p> In [<CitationRef CitationID="CR21">21</CitationRef>] and [<CitationRef CitationID="CR22">22</CitationRef>], we proved the Kastler–Kalau–Walze type theorem for the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3236_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(J\)</EquationSource> </InlineEquation>-twist <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3236_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(D_{J}\)</EquationSource> </InlineEquation> of the Dirac operator on <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3236_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\)</EquationSource> </InlineEquation>-dimensional, <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3236_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(4\)</EquationSource> </InlineEquation>-dimensional, and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3236_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(6\)</EquationSource> </InlineEquation>-dimensional almost product Riemannian spin manifolds with boundary. In this paper, we generalize our previous conclusions and establish the proof of the general Kastler–Kalau–Walze type theorem for the <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3236_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(J\)</EquationSource> </InlineEquation>-twist <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3236_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(D_{J}\)</EquationSource> </InlineEquation> of the Dirac operator on any even-dimensional almost product Riemannian spin manifold with boundary. </p> <p> <b> DOI</b> 10.1134/S1061920824601204 </p>

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The General Kastler–Kalau–Walze Type Theorem for the \(J\)-Twist \(D_{J}\) of the Dirac Operator

  • Siyao Liu,
  • Yong Wang

摘要

Abstract

In [21] and [22], we proved the Kastler–Kalau–Walze type theorem for the \(J\) -twist \(D_{J}\) of the Dirac operator on \(3\) -dimensional, \(4\) -dimensional, and \(6\) -dimensional almost product Riemannian spin manifolds with boundary. In this paper, we generalize our previous conclusions and establish the proof of the general Kastler–Kalau–Walze type theorem for the \(J\) -twist \(D_{J}\) of the Dirac operator on any even-dimensional almost product Riemannian spin manifold with boundary.

DOI 10.1134/S1061920824601204