Conformal vector field and gradient Einstein solitons on ?-Einstein cosymplectic manifolds

초록

In this paper, we characterize the ?-Einstein cosymplectic manifolds with the gradient Einstein solitons and the conformal vector fields. It is proven that if an ?-Einstein cosymplectic manifold M2n+1 of dimension 2n + 1 with n > 1 admits a gradient Einstein soliton, then either M2n+1 is Ricci flat or the gradient of Einstein potential function is pointwise collinear with the Reeb vector field of M2n+1. Also, we prove that if M2n+1 admits a conformal vector field W, then either M2n+1 is Ricci flat or W is homothetic. We also establish that a conformal vector field W on M2n+1 is a strict infinitesimal contact transformation, provided the scalar curvature of M2n+1 is constant. Finally, the non-trivial examples of cosymplectic manifolds admitting the gradient Einstein solitons are given.

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