Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature

Yuhang Liu*, Yunchu Dai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in Rn. They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces. In particular, they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume, which can be seen as the higher-dimensional generalization of the pseudo-sphere.
Original languageEnglish
JournalChinese Annals of Mathematics. Series B
Volume43
Issue number3
Publication statusPublished - 18 Aug 2022

Keywords

  • Differential geometry
  • Gauss-Kronecker curvature
  • Ordinary Differential Equation (ODE)

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