In this paper, we investigate the behavior of Ricci solitons under Generalized $\mathcal{D}$-conformal deformation on cosymplectic manifolds. We derive expressions for the deformation tensor and explore the changes that occur to the soliton vector field and the soliton constant under deformation. Our results reveal interesting insights into the behavior of Ricci solitons on almost contact metric manifolds and highlight the differences between the various classes of manifolds.
In this article, we investigate the behavior of Ricci solitons under D-isometric deformations on a class of Riemannian manifolds. A D-isometry is a diffeomorphism that preserves the distance function induced by a Riemannian metric up to a constant factor. We consider a family of Riemannian metrics g on a manifold M that are related by D-isometric deformations, and we study the Ricci soliton equation on each metric g. We show that under certain conditions on the deformation function, the solutions to the Ricci-Soliton equation on each metric g are invariant. In particular, we obtain a family of Ricci-Solitons that are related by a scaling factor under D-isometric deformations. We also provide explicit examples of D-isometric deformations and compute the corresponding Ricci-Solitons.
2000 Mathematics Subject Classification. 53C15, 53C25, 53D10.
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