Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form

Abstract: Lorantzian trans-Sasakian space form is a special type of space form in which the nature of even and odd dimensional space form both exist. Various curvature tensors with respect to Levi-Civita connection on the space form are derived in this paper. We have shown that if an odd-dimensional Lorentzian trans-Sasakian space form admits a hyperbolic Ricci soliton and hyperbolic conformal Ricci soliton then they will be ${\eta}$-Einstein. We also obtained the conditions for the solitons to be expanding, steady or shrinking. Finally, an example has been constructed which justifies the results obtained.