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arXiv · 2110.14103

Gradient Ricci solitons carrying a closed conformal vector field

J. F. Siva Filho·R. Sharma
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Abstract

We show that a complete gradient Ricci soliton $(M^n,\,g)$ with constant scalar curvature and a non-parallel closed conformal vector field is isometric to either the Euclidean space, or an Euclidean sphere, or negatively Einstein warped product of the real line with a complete non-positively Einstein manifold. Moreover, we show that a K\"ahler gradient Ricci soliton of real dimension $\ge 4$, with a non-parallel closed conformal real vector field is Ricci-flat (Calabi-Yau) and is flat in dimension 4. Finally, we show that a Ricci soliton whose associated 1-form is harmonic, has constant scalar curvature.

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J. F. Siva Filho, R. Sharma. 2021-10-27. Gradient Ricci solitons carrying a closed conformal vector field. https://arxiv.org/abs/2110.14103

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