Gradient almost Ricci solitons on multiply warped product manifolds

  • S. Günsen Aydin Adnan Menderes University, Kepez Mevkii Efeler, 09010 Aydin, Turkey
  • L. Onat Aydin Adnan Menderes University, Kepez Mevkii Efeler, 09010 Aydin, Turkey
Keywords: multiply warped product, gradient almost Ricci soliton, generalized quasi-Einstein manifold, conformal vector field
Published online: 2021-08-22

Abstract


In this paper, we investigate multiply warped product manifold \[M =B\times_{b_1} F_1\times_{b_2} F_2\times_{b_3} \ldots \times_{b_m} F_m\] as a gradient almost Ricci soliton. Taking $b_i=b$ for $1\leq i \leq m$ lets us to deduce that potential field depends on $B$. With this idea we also get a rigidity result and show that base is a generalized quasi-Einstein manifold if $\nabla b$ is conformal.

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How to Cite
(1)
GünsenS.; OnatL. Gradient Almost Ricci Solitons on Multiply Warped Product Manifolds. Carpathian Math. Publ. 2021, 13, 386-394.