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arXiv · 1711.11455

On Warped Product Gradient Yamabe Soliton

Willian I. Tokura·Levi Adriano·Romildo Pina
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Abstract

In this paper, we provide a necessary and sufficient conditions for the warped product $M=B\times_f F$ to be a gradient Yamabe soliton when the base is conformal to an n-dimensional pseudo-Euclidean space, which are invariant under the action of an (n-1)-dimensional translation group, and the fiber F is scalar-constant. As application, we obtain solutions in steady case with fiber scalar-flat. Besides, on the warped product we consider the potential function as separable variables and obtain some characterization of the base and the fiber.

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Willian I. Tokura, Levi Adriano, Romildo Pina. 2017-11-30. On Warped Product Gradient Yamabe Soliton. https://arxiv.org/abs/1711.11455

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