允许闭共形向量场的广义m-拟Einstein流形

IF 1 3区 数学 Q1 MATHEMATICS
Rahul Poddar, S. Balasubramanian, Ramesh Sharma
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引用次数: 0

摘要

我们研究了一个具有有限m的完全连通广义m-拟Einstein流形m,承认了一个非同胚的、非平行的、完全闭合的共形向量场V,并证明了m与一个圆球面等距,或者Ricci张量可以用开稠密子集上的共形数据显式表示。在后一种情况下,我们证明了M是开实区间与爱因斯坦流形的翘曲乘积;此外,它在维度4上是保形平坦的并且在维度>;3.接下来,对于具有非平行闭合共形矢量场的梯度Ricci几乎孤立子,我们获得了Ricci张量的相同显式表达式和类似的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Generalized m-Quasi-Einstein manifolds admitting a closed conformal vector field

We study a complete connected generalized m-quasi-Einstein manifold M with finite m, admitting a non-homothetic, non-parallel, complete closed conformal vector field V, and show that either M is isometric to a round sphere, or the Ricci tensor can be expressed explicitly in terms of the conformal data over an open dense subset. In the latter case, we prove that M is a warped product of an open real interval with an Einstein manifold; furthermore, it is conformally flat in dimension 4 and has vanishing Cotton and Bach tensors in dimension > 3. Next, we obtain the same explicit expression for the Ricci tensor, and analogous results, for a gradient Ricci almost soliton endowed with a non-parallel closed conformal vector field.

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来源期刊
CiteScore
2.10
自引率
10.00%
发文量
99
审稿时长
>12 weeks
期刊介绍: This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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