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<p>For a Finsler manifold with the Ricci curvature bounded below by a positive number and nonnegative <i>S</i>-curvature, we obtain Cheng type maximal diameter theorem and show that it must be isometric to a standard Finsler sphere. In particular, when the Finsler manifold is an <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2165_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\((\alpha ,\beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-manifold, then it attains its maximal diameter if and only if it is isometric to a standard Randers sphere, and further the metric can be determined analytically. The proof is based on the Laplacian comparison theorem, the volume comparison theorem and the so-called reverse technique in Finsler geometry.</p>

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The Maximal Diameter Theorem on Finsler Manifolds II

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Songting E-Yin

摘要

For a Finsler manifold with the Ricci curvature bounded below by a positive number and nonnegative S-curvature, we obtain Cheng type maximal diameter theorem and show that it must be isometric to a standard Finsler sphere. In particular, when the Finsler manifold is an \((\alpha ,\beta )\) ( α , β ) -manifold, then it attains its maximal diameter if and only if it is isometric to a standard Randers sphere, and further the metric can be determined analytically. The proof is based on the Laplacian comparison theorem, the volume comparison theorem and the so-called reverse technique in Finsler geometry.