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Isometries on almost Ricci–Yamabe solitons

Authors :
Mohan Khatri
C. Zosangzuala
Jay Prakash Singh
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