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arXiv · 2101.03896

Some characterizations of $\rho$-Einstein solitons

Absos Ali Shaikh·Antonio W. Cunha·Prosenjit Mandal
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Abstract

In this article we have showed that a gradient $\rho$-Einstein soliton with a vector field of bounded norm and satisfying some other conditions is isometric to the Euclidean sphere. Later, we have proved that a non-trivial complete gradient $\rho$-Einstein soliton with finite weighted Dirichlet integral and certain restriction on Ricci curvature must be of constant scalar curvature and steady Ricci flat. Finally, we have proved that a non-shrinking or non-expanding gradient traceless Ricci soliton possessing some conditions must be steady.

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Absos Ali Shaikh, Antonio W. Cunha, Prosenjit Mandal. 2020-12-08. Some characterizations of $\rho$-Einstein solitons. https://doi.org/10.1016/j.geomphys.2021.104270

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