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<p>In this paper, firstly we prove that all <i>R</i>-quadratic manifolds with nonzero scalar flag curvature must be Riemannian spaces with constant sectional curvature. We introduce the definition of the scalar curvature condition. We can prove that if (<i>M</i>,&#xa0;<i>F</i>) is a Randers space with constant flag curvature <i>K</i> satisfying the scaler curvature condition, then (<i>M</i>,&#xa0;<i>F</i>) is either a locally Minkowskian space with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_430_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(K=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> or a Riemannian space with constant sectional curvature <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_430_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(K\ne 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>≠</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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On the Flag Curvature of Finsler Manifolds

  • 期刊论文

  • 发表日期：

    2025年8月3日

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  • Jintang Li

摘要

In this paper, firstly we prove that all R-quadratic manifolds with nonzero scalar flag curvature must be Riemannian spaces with constant sectional curvature. We introduce the definition of the scalar curvature condition. We can prove that if (M, F) is a Randers space with constant flag curvature K satisfying the scaler curvature condition, then (M, F) is either a locally Minkowskian space with \(K=0\) K = 0 or a Riemannian space with constant sectional curvature \(K\ne 0\) K ≠ 0 .