黄金空间形式和某些 CR 子曼形中的弱爱因斯坦等价性

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2023-12-01 DOI:10.1515/ms-2023-0117

Jihun Kim, Jeonghyeong Park, Bayram Şahin

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引用次数: 1

摘要

摘要众所周知，黄金空间形式可能不是爱因斯坦流形。本文证明了黄金空间形式是爱因斯坦流形的条件等同于弱爱因斯坦流形。此外，本文还研究了黄金空间的 CR 子曼形体的部分大地平行性和循环平行性，并确定了黄金分割曲率不变的情况。此外，还研究了具有半平面法连接的 CR 子曼形体，并得到了一个不等式。我们还检验了该不等式的相等情况。我们还考虑了金黎曼流形的全脐 CR 子流形，并证明了在某些条件下，这类子流形是全测地线。此外，我们还得到了一个涉及 CR 子曼形体标量曲率的不等式，并检验了黄金空间形式中外球的存在性。

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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Weakly Einstein Equivalence in a Golden Space Form and Certain CR-submanifolds

ABSTRACT It is known that the Golden space form may not be an Einstein manifold. In this paper, it is shown that the condition to be Einstein for a Golden space form is equivalent to being weakly Einstein. In addition, the partial geodesic and cyclic parallelism of the CR-submanifolds of a Golden space are examined, and the case of the constant Golden sectional curvature is determined. Moreover, the CR-submanifolds with semi-flat normal connection are studied and an inequality is obtained. The equality case of this inequality is also checked. We also consider the totally umbilical CR-submanifold of Golden Riemannian manifolds and show that such submanifolds are totally geodesic under certain conditions. Furthermore, we obtain an inequality involving the scalar curvature of CR-submanifold and check the existence of extrinsic spheres in Golden space forms.

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.