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Isometries on almost Ricci–Yamabe solitons

Authors :
Mohan Khatri
C. Zosangzuala
Jay Prakash Singh
Source :
Arabian Journal of Mathematics. 12:127-138
Publication Year :
2022
Publisher :
Springer Science and Business Media LLC, 2022.

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.

Subjects

Subjects :
General Mathematics

Details

ISSN :
21935351 and 21935343
Volume :
12
Database :
OpenAIRE
Journal :
Arabian Journal of Mathematics
Accession number :
edsair.doi...........ac89d087a3615b3bf339388fa6ffa238
Full Text :
https://doi.org/10.1007/s40065-022-00404-x