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<p>In this paper, we study the isoparametric hypersurfaces in a class of conic Kropina manifolds. For a conic Kropina metric <i>F</i>(<i>x</i>,&#xa0;<i>y</i>) on a manifold <i>M</i> with navigation data (<i>h</i>,&#xa0;<i>W</i>), and a vector field <i>V</i> with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_339_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="101" /> </InlineMediaObject> <EquationSource Format="TEX">\(F(x,-V)=1\)</EquationSource> </InlineEquation>, let <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_339_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tilde{F}=\tilde{F}(x, y)\)</EquationSource> </InlineEquation> be the solution of navigation data (<i>F</i>,&#xa0;<i>V</i>). By studying the principal curvatures of anisotropic submanifolds in Kropina space&#xa0;<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_339_Article_IEq3.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\((M, \tilde{F})\)</EquationSource> </InlineEquation> with the navigation data&#xa0;(<i>h</i>,&#xa0;<i>W</i>), we find that Kropina space <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_339_Article_IEq4.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="99" /> </InlineMediaObject> <EquationSource Format="TEX">\((M, \tilde{F}, d\mu _{BH})\)</EquationSource> </InlineEquation> and the corresponding Riemannian space (<i>M</i>,&#xa0;<i>h</i>) have the same isoparametric hypersurfaces. Moreover, we give a complete classification of isoparametric hypersurfaces in Kropina space <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_339_Article_IEq4.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="99" /> </InlineMediaObject> <EquationSource Format="TEX">\((M, \tilde{F}, d\mu _{BH})\)</EquationSource> </InlineEquation> with constant flag curvature.</p>

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Isoparametric Hypersurfaces in a Class of Conic Kropina Manifolds by Navigation Data

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  • 发表日期：

    2025年10月20日

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  • Peilong Dong

摘要

In this paper, we study the isoparametric hypersurfaces in a class of conic Kropina manifolds. For a conic Kropina metric F(x, y) on a manifold M with navigation data (h, W), and a vector field V with \(F(x,-V)=1\) , let \(\tilde{F}=\tilde{F}(x, y)\) be the solution of navigation data (F, V). By studying the principal curvatures of anisotropic submanifolds in Kropina space  \((M, \tilde{F})\) with the navigation data (h, W), we find that Kropina space \((M, \tilde{F}, d\mu _{BH})\) and the corresponding Riemannian space (M, h) have the same isoparametric hypersurfaces. Moreover, we give a complete classification of isoparametric hypersurfaces in Kropina space \((M, \tilde{F}, d\mu _{BH})\) with constant flag curvature.