一类量沿ricci-bourguignon流的演化和单调性

Pub Date : 2019-01-01 DOI:10.4134/JKMS.J180525

Farzad Daneshvar, A. Razavi

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引用次数: 4

摘要

．本文考虑了Ricci-Bourguignon流和归一化Ricci-Bourguignon流下最低常数λ ba (g)的单调性，使得方程-∆u + au log u + bRu = λ ba (g) u， (cid:82) m2dv = 1有正解，其中a和b是两个实常数。在Ricci-Bourguignon流和归一化Ricci-Bourguignon流下构造了各种单调量。此外，我们还证明了在Ricci- Bourguignon流下演化的紧致稳定呼吸区应该是Ricci-flat。

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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EVOLUTION AND MONOTONICITY FOR A CLASS OF QUANTITIES ALONG THE RICCI-BOURGUIGNON FLOW

. In this paper we consider the monotonicity of the lowest constant λ ba ( g ) under the Ricci-Bourguignon ﬂow and the normalized Ricci- Bourguignon ﬂow such that the equation − ∆ u + au log u + bRu = λ ba ( g ) u with (cid:82) M u 2 dV = 1 , has positive solutions, where a and b are two real con-stants. We also construct various monotonic quantities under the Ricci- Bourguignon ﬂow and the normalized Ricci-Bourguignon ﬂow. Moreover, we prove that a compact steady breather which evolves under the Ricci- Bourguignon ﬂow should be Ricci-ﬂat.

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