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Isometries on almost Ricci–Yamabe solitons
- Source :
- Arabian Journal of Mathematics, Vol 12, Iss 1, Pp 127-138 (2022)
- Publication Year :
- 2022
- Publisher :
- SpringerOpen, 2022.
-
Abstract
- Abstract The purpose of the present paper is to examine the isometries of almost Ricci–Yamabe solitons. Firstly, the conditions under which a compact gradient almost Ricci–Yamabe soliton is isometric to Euclidean sphere $$S^n(r)$$ S n ( r ) are obtained. Moreover, we have shown that the potential f of a compact gradient almost Ricci–Yamabe soliton agrees with the Hodge–de Rham potential h. Next, we studied complete gradient almost Ricci–Yamabe soliton with $$\alpha \ne 0$$ α ≠ 0 and non-trivial conformal vector field with non-negative scalar curvature and proved that it is either isometric to Euclidean space $$E^n$$ E n or Euclidean sphere $$S^n.$$ S n . Also, solenoidal and torse-forming vector fields are considered. Lastly, some non-trivial examples are constructed to verify the obtained results.
Details
- Language :
- English
- ISSN :
- 21935343 and 21935351
- Volume :
- 12
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Arabian Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.fc093068b7d4f36b67b46c18963f7c1
- Document Type :
- article
- Full Text :
- https://doi.org/10.1007/s40065-022-00404-x