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<p>In this paper, we introduce a new type of tensor on a Weyl manifold, which we named the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \mathcal {A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">A</mi> </math></EquationSource> </InlineEquation> tensor. After investigating the properties of this tensor, we obtain the necessary and sufficient condition for a conformal mapping to preserve the proposed tensor. Moreover, we demonstrate that in Einstein-Weyl space, if the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( \mathcal {A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">A</mi> </math></EquationSource> </InlineEquation> tensor is a conformal invariant, then the scalar curvature <i>W</i> is also a conformal invariant, and vice versa.</p>

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The special tensor on Weyl manifolds

  • 期刊论文

  • 发表日期：

    2025年10月25日

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  • S. Aynur Uysal,
  • Hülya Bağdatlı Yılmaz

摘要

In this paper, we introduce a new type of tensor on a Weyl manifold, which we named the \( \mathcal {A}\) A tensor. After investigating the properties of this tensor, we obtain the necessary and sufficient condition for a conformal mapping to preserve the proposed tensor. Moreover, we demonstrate that in Einstein-Weyl space, if the \( \mathcal {A}\) A tensor is a conformal invariant, then the scalar curvature W is also a conformal invariant, and vice versa.