Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature

Yuhang Liu; Yunchu Dai

doi:10.1007/s11401-022-0324-7

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

1 Citation (Scopus)

60 Downloads (Pure)

Abstract

The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in ℝ ⁿ. 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
Pages (from-to)	343-358
Number of pages	16
Journal	Chinese Annals of Mathematics. Series B
Volume	43
Issue number	3
DOIs	https://doi.org/10.1007/s11401-022-0324-7
Publication status	Published - May 2022

Keywords

Differential geometry
Gauss-Kronecker curvature
Ordinary Differential Equation (ODE)
53A07
Ordinary differential equation

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10.1007/s11401-022-0324-7

Yuhang Yunchu cambFinal published version, 233 KBLicence: Unspecified

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

abstract = "The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in ℝ n. 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.",

keywords = "Differential geometry, Gauss-Kronecker curvature, Ordinary Differential Equation (ODE), 53A07, Ordinary differential equation",

author = "Yuhang Liu and Yunchu Dai",

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AU - Liu, Yuhang

AU - Dai, Yunchu

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N2 - The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in ℝ n. 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 ℝ n. 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)

KW - 53A07

KW - Ordinary differential equation

UR - https://www.scopus.com/pages/publications/85140648898

U2 - 10.1007/s11401-022-0324-7

DO - 10.1007/s11401-022-0324-7

M3 - Article

SN - 0252-9599

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EP - 358

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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