Compact almost Co-Kahler manifolds and Ricci-Yamabe solitons

초록

In this article we establish that if the metric g of a compact almost Co-Kahler manifold <spacing diaeresis> M2n+1 is a Ricci-Yamabe soliton whose potential vector field is point-wise collinear with the characteristic vector field, then M2n+1 is a K-almost Co-Kahler manifold under certain condition, whereas in dimension three <spacing diaeresis> the restriction is not required. It is prove that if a (2n+1)-dimensional (kappa, mu)-almost Co-Kahler manifold <spacing diaeresis> M with kappa < 0 admits a Ricci-Yamabe soliton of gradient type, then M is a N(kappa)-almost Co-Kahler manifold. <spacing diaeresis> We also show the non-existence of gradient Ricci-Yamabe structures with D Psi = (zeta Psi)zeta on a compact (kappa, mu)- almost Co-Kahler manifold with <spacing diaeresis> kappa < 0. Then we establish that in a Co-Kahler 3-manifold <spacing diaeresis> M-3 with gradient Ricci-Yamabe solitons, the scalar curvature of the manifold is constant and also, either M-3 is flat, or the gradient of the potential function is collinear with the characteristic vector field zeta. Finally, we construct two non-trivial examples to ensure the existence of such solitons.

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