CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM*

doi:10.1007/s10473-023-0606-5

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2413-2429.doi: 10.1007/s10473-023-0606-5

CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM^*

Huiyang XU, Cece LI^†

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China

收稿日期:2022-06-10 修回日期:2023-05-20 发布日期:2023-12-08
通讯作者: †Cece LI, E-mail: ceceli@haust.edu.cn
作者简介:Huiyang XU, E-mail: xuhuiyang@haust.edu.cn
基金资助:
This work was supported by the NNSF of China (12101194, 11401173).

CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM^*

Huiyang XU, Cece LI^†

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China

Received:2022-06-10 Revised:2023-05-20 Published:2023-12-08
Contact: †Cece LI, E-mail: ceceli@haust.edu.cn
About author:Huiyang XU, E-mail: xuhuiyang@haust.edu.cn
Supported by:
This work was supported by the NNSF of China (12101194, 11401173).

摘要/Abstract

摘要： In this paper, we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric. As a main result, we classify these hypersurfaces as not being of a flat affine metric. In particular, 2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.

关键词: affine hypersurface, semi-parallel cubic form, Levi-Civita connection, conformally flat, warped product

Abstract: In this paper, we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric. As a main result, we classify these hypersurfaces as not being of a flat affine metric. In particular, 2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.

Key words: affine hypersurface, semi-parallel cubic form, Levi-Civita connection, conformally flat, warped product

中图分类号:

53A15

Huiyang XU, Cece LI. CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM^*[J]. 数学物理学报(英文版), 2023, 43(6): 2413-2429.

Huiyang XU, Cece LI. CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2413-2429.

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CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM^*

CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM^*

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