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

Year 2024, Volume: 7 Issue: 1, 1 - 11, 18.03.2024

Uday Chand De , Tarak Mandal , Avijit Sarkar

https://doi.org/10.32323/ujma.1381621

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

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