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<p>As an extension of equiaffine hyperspheres in equiaffine differential geometry, Tchebychev hypersurfaces in relative geometry have been extensively studied. In this paper, we focus on Tchebychev hypersurfaces in Calabi affine geometry and establish a complete classification of Calabi Tchebychev hypersurfaces with constant sectional curvature in affine space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^{n+1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n=2,3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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On Calabi Tchebychev Hypersurfaces with Constant Sectional Curvature

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Yalin Sun,
  • Ruiwei Xu,
  • Mengguo Zhang

摘要

As an extension of equiaffine hyperspheres in equiaffine differential geometry, Tchebychev hypersurfaces in relative geometry have been extensively studied. In this paper, we focus on Tchebychev hypersurfaces in Calabi affine geometry and establish a complete classification of Calabi Tchebychev hypersurfaces with constant sectional curvature in affine space \(\mathbb {R}^{n+1}\) R n + 1 for \(n=2,3\) n = 2 , 3 .