- Universal Journal of Mathematics and Applications
- Cilt: 7 Sayı: 1
- Miao-Tam Equation and Ricci Solitons on Three-Dimensional Trans-Sasakian Generalized Sasakian Space-...
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 : 104 | Download : 153
Publication Date : 2024-03-18
Article Type : Research
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