2025 / March Volume 20 No.1
Compact hyperbolic Ricci solitons with constant scalar curvature and 2-conformal vector fields
| Published Date |
2025 / March
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| Title | Compact hyperbolic Ricci solitons with constant scalar curvature and 2-conformal vector fields |
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| Pagination | 79-93 |
| Abstract | In this paper, we consider a non-trivial compact hyperbolic Ricci soliton $(N^n,g,X,\lambda,\mu)$. Letting the vector field $X$ to be a $2-$conformal field, we find two integral equations for compact oriented hyperbolic Ricci solitons with $2-$conformal potential vector field. We show that such a manifold with constant scalar curvature is isometric to the Euclidean sphere $\mathbb{S}^n$. As a consequence, our results indicate that $X$ is gradient. Moreover, $X$ can be decomposed (according to the Hodge-de Rham theorem) into the sum of a Killing vector field and the gradient of a suitable smooth function on $N$.
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| DOI | |
| AMS Subject Classification |
53Bxx, 53Cxx, 53Exx
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| Received |
2024-09-16
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