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Ricci soliton on a class of Riemannian manifolds under $D$-isometric deformation
by Delloum Adel   Beldjilali Gherici  

Vol. 18 No. 3 (2023) P.269~P.282
DOI: https://doi.org/10.21915/BIMAS.2023302
  10.21915/BIMAS.2023302

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.


KEYWORDS
Riemannian manifolds, Ricci solitons, Deformation of metrics.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 53C15, 53C25, 53D10

MILESTONES

Received: 2023-05-31
Revised :
Accepted:


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