Miao-Tam Equation and Ricci Solitons on Three-Dimensional Trans-Sasakian Generalized Sasakian Space-Forms

Authors : Uday Chand De, Tarak Mandal, Avijit Sarkar

Pages : 1-11

Doi:10.32323/ujma.1381621

View : 111 | Download : 161

Publication Date : 2024-03-18

Article Type : Research Paper

Abstract :The aim of the present article is to characterize some properties of the Miao-Tam equation on three-dimensional generalized Sasakian space-forms with trans-Sasakian structures. It has been proved that in such space-forms if the Miao-Tam equation admits non-trivial solution, then the metric of the space form must be a gradient Ricci soliton. We have derived that a non-trivial solution of the Fischer-Marsden equation does not exist on the said space-forms. We have also investigated certain features of Ricci solitons and gradient Ricci solitons. At the end of the article, we construct an example to verify the obtained results.
Keywords : Generalized Sasakian space forms, Gradient Ricci solitons, Miao Tam equation, Sasakian space forms, Trans Sasakian manifolds