具有半平行三次形式的共形平坦仿射超曲面

IF 1.2 4区数学 Q1 MATHEMATICS Acta Mathematica Scientia Pub Date : 2023-11-06 DOI:10.1007/s10473-023-0606-5

Huiyang Xu, Cece Li

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引用次数: 2

摘要

本文研究了具有消失Weyl曲率张量和相对于仿射度量的Levi-Civita连接的半平行三次形式的局部强凸仿射超曲面。作为一个主要结果，我们将这些超曲面分类为不是平面仿射度量。特别地，完全确定了具有半平行三次形式的2和3维局部强凸仿射超曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Conformally flat affine hypersurfaces with semi-parallel cubic form

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.

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.