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arXiv · 2503.24337

On gradient $\rho$-Einstein solitons with Bach tensor radially nonnegative

Maria Andrade·Valter Borges·Hiuri Reis
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Abstract

In this paper, we study $n$-dimensional gradient $\rho$-Einstein solitons whose Bach tensor is radially nonnegative. Under this assumption, we show that such $\rho$-Einstein solitons are locally warped products of an interval and an Einstein manifold, provided either $\rho\neq0$ or $\rho=0$ and the soliton is rectifiable. We obtain as a consequence that these solitons must have harmonic Weyl tensor and vanishing Bach tensor. We also finish the classification of complete locally conformally flat steady $\rho$-Einstein solitons and classify these manifolds when their Bach tensor is radially nonnegative and $n\in\{3,4\}$.

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Maria Andrade, Valter Borges, Hiuri Reis. 2025-03-31. On gradient $\rho$-Einstein solitons with Bach tensor radially nonnegative. https://arxiv.org/abs/2503.24337

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