Research Information System
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, vol.29, no.2, 2026 (SCI-Expanded, Scopus)
We investigate eta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-Ricci-Bourguignon soliton to be Killing. Finally, we prove that if a compact, orientable and without boundary eta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-Ricci-Bourguignon solitons admits a potential function satisfying the Hodge-de Rham decomposition theorem, then the potential function is harmonic.