https://doi.org/10.1140/epjp/s13360-022-02399-y
Regular Article
Investigations on solitons in 
-gravity
1
Department of Mathematics, Kabi Sukanta Mahavidyalaya, The University of Burdwan, P.O.-Angus, Hooghly, 712221, Bhadreswar, West Bengal, India
2
Department of Mathematics, University of Calcutta, Calcutta, West Bengal, India
Received:
26
June
2021
Accepted:
17
January
2022
Published online:
27
January
2022
The prime purpose of this paper is to characterize the -gravity, when Ricci solitons, gradient Ricci solitons and gradient Yamabe solitons, respectively are its metrics. At first, the existence of gradient Yamabe solitons is established by some non-trivial examples. We prove that if 
be a Ricci soliton in a perfect fluid spacetime with constant Ricci scalar in -gravity, then the perfect fluid spacetime represents a dark matter era under certain restrictions on the vector field 
. Besides, we investigate gradient Ricci solitons and gradient Yamabe solitons in -gravity, respectively. As a result, we acquire some significant theorems. Finally, a(t), the scale factor is obtained when spatially flat Robertson-Walker spacetime admits Ricci solitons and gradient Yamabe solitons.
A correction to this article is available online at https://doi.org/10.1140/epjp/s13360-022-02440-0.
Copyright comment corrected publication 2022
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. corrected publication 2022
