Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature

Yuhang Liu; Yunchu Dai

Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature

Yuhang Liu^*, Yunchu Dai

^*Corresponding author for this work

Department of Foundational Mathematics

Stanford University

Research output: Contribution to journal › Article › peer-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 language	English
Journal	Chinese Annals of Mathematics. Series B
Volume	43
Issue number	3
Publication status	Published - 18 Aug 2022

Keywords

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

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title = "Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature",

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.",

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author = "Yuhang Liu and Yunchu Dai",

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T1 - Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature

AU - Liu, Yuhang

AU - Dai, Yunchu

PY - 2022/8/18

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N2 - 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.

AB - 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.

KW - Differential geometry

KW - Gauss-Kronecker curvature

KW - Ordinary Differential Equation (ODE)

M3 - Article

SN - 0252-9599

VL - 43

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 3

ER -

Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature

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Keywords

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