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Properties of Warped Product Gradient Yamabe Solitons

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Abstract

In this paper, we study gradient Yamabe solitons realized as warped product manifolds. We apply the maximum principle to find lower bound estimates for both the potential function of the soliton and the scalar curvature of the warped product manifold. By slightly modifying Li–Yau’s technique, we can handle the drifted Laplacian and thus find different gradient estimates for the warping function according to the sign of the (constant) scalar curvature of the fiber manifold. We close the article with a theorem stating the nonexistence of gradient Yamabe solitons on top of warped products with a base manifold satisfying certain analytical hypothesis.

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Acknowledgements

The authors would like to thank the referee for his careful reading and valuable suggestions.

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Authors and Affiliations

  1. Universidade Federal da Grande Dourados, FACET, 79825-070, Dourados–MS, Brazil

    Willian Tokura

  2. Universidade Federal de Goiás, IME, 131, 74001–970, Goiânia–GO, Brazil

    Marcelo Barboza, Levi Adriano & Romildo Pina

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  1. Willian Tokura
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  2. Marcelo Barboza
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  3. Levi Adriano
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  4. Romildo Pina
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All authors wrote and reviewed the main manuscript text.

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Correspondence to Willian Tokura.

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Tokura, W., Barboza, M., Adriano, L. et al. Properties of Warped Product Gradient Yamabe Solitons. Mediterr. J. Math. 20, 248 (2023). https://doi.org/10.1007/s00009-023-02451-w

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  • DOI: https://doi.org/10.1007/s00009-023-02451-w

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