Scholarlink

<p>We investigate <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Ricci-Bourguignon solitons on compact Riemannian manifolds. The rigidity results are proven under the condition that the solitons are Einstein manifolds. Furthermore, we provide a necessary and sufficient condition for the potential vector field on a non-trivial closed <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Ricci-Bourguignon soliton to be Killing. Finally, we prove that if a compact, orientable and without boundary <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Ricci-Bourguignon solitons admits a potential function satisfying the Hodge-de Rham decomposition theorem, then the potential function is harmonic.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Compact \(\eta \)-Ricci-Bourguignon Solitons

  • 期刊论文

  • 发表日期：

    2026年4月12日

查看全文
  • Moctar Traore

摘要

We investigate \(\eta \) η -Ricci-Bourguignon solitons on compact Riemannian manifolds. The rigidity results are proven under the condition that the solitons are Einstein manifolds. Furthermore, we provide a necessary and sufficient condition for the potential vector field on a non-trivial closed \(\eta \) η -Ricci-Bourguignon soliton to be Killing. Finally, we prove that if a compact, orientable and without boundary \(\eta \) η -Ricci-Bourguignon solitons admits a potential function satisfying the Hodge-de Rham decomposition theorem, then the potential function is harmonic.