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<p>Almost Finsler manifolds and partial Finsler manifolds are introduced, extending the standard definition of a Finsler manifold to allow for a nontrivial slit containing points fixed under homogeneous scaling and for metrics where the fundamental tensor has nonpositive eigenvalues. The bipartite spaces offer examples of comparatively simple almost Finsler manifolds and partial Finsler manifolds with physics applications. Special cases are the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{\textbf{a}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">a</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({{\textbf{b}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">b</mi> </math></EquationSource> </InlineEquation> spaces, which have almost Finsler norms and partial Finsler norms formed from a Riemannian norm and a 1-form. The indicatrix union of the almost Finsler <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({{\textbf{a}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">a</mi> </math></EquationSource> </InlineEquation> manifolds equals the indicatrix union of Randers spaces. Characteristic tensors that vanish for bipartite spaces and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({{\textbf{b}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">b</mi> </math></EquationSource> </InlineEquation> spaces are obtained and expressed using geometric quantities. These tensors are generalizations of the Matsumoto tensor, which vanishes on Randers and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({{\textbf{a}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">a</mi> </math></EquationSource> </InlineEquation> spaces.</p>

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Characteristic Tensors for Almost Finsler Manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月12日

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  • James F. Davis,
  • Benjamin R. Edwards,
  • V. Alan Kostelecký

摘要

Almost Finsler manifolds and partial Finsler manifolds are introduced, extending the standard definition of a Finsler manifold to allow for a nontrivial slit containing points fixed under homogeneous scaling and for metrics where the fundamental tensor has nonpositive eigenvalues. The bipartite spaces offer examples of comparatively simple almost Finsler manifolds and partial Finsler manifolds with physics applications. Special cases are the \({{\textbf{a}}}\) a and \({{\textbf{b}}}\) b spaces, which have almost Finsler norms and partial Finsler norms formed from a Riemannian norm and a 1-form. The indicatrix union of the almost Finsler \({{\textbf{a}}}\) a manifolds equals the indicatrix union of Randers spaces. Characteristic tensors that vanish for bipartite spaces and \({{\textbf{b}}}\) b spaces are obtained and expressed using geometric quantities. These tensors are generalizations of the Matsumoto tensor, which vanishes on Randers and \({{\textbf{a}}}\) a spaces.