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Ricci soliton on a class of Riemannian manifolds under D-isometric deformation.

Article scientifique 2023 Anglais

Résumé

Abstract 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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AdelDelloum, A., Beldjilali, G. (2023). Ricci soliton on a class of Riemannian manifolds under D-isometric deformation.. https://doi.org/10.21203/rs.3.rs-2768828/v1

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Auteur(s)

AdelDelloum AdelDelloum Gherici Beldjilali

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