In this paper, we define a new geometric vector field on (semi-)Riemannaian manifolds. These new vector fields on 3-dimensional Walker manifolds will be derived. Then, we study Ricci solitons admitting this new vector field (called semi-Killing vector field) as their potential. In Riemannain setting, we prove that Ricci solitons with semi-Killing potential vector field are Einstein. Also, It will be shown that such Lorentzian solitons have constant scalar curvature. Finally, application of this new structure in physics will be investigated. In fact, we propose that semi-Killing vector fields are in relation to the notion of dark energy in general relativity.
Shamkhali, F., Fasihi Ramandi, G., & Azami, S. (2024). Geometry of Ricci solitons admitting a new geometric vector field. AUT Journal of Mathematics and Computing, (), -. doi: 10.22060/ajmc.2024.23142.1234
MLA
Farzaneh Shamkhali; Ghodratallah Fasihi Ramandi; Shahroud Azami. "Geometry of Ricci solitons admitting a new geometric vector field". AUT Journal of Mathematics and Computing, , , 2024, -. doi: 10.22060/ajmc.2024.23142.1234
HARVARD
Shamkhali, F., Fasihi Ramandi, G., Azami, S. (2024). 'Geometry of Ricci solitons admitting a new geometric vector field', AUT Journal of Mathematics and Computing, (), pp. -. doi: 10.22060/ajmc.2024.23142.1234
VANCOUVER
Shamkhali, F., Fasihi Ramandi, G., Azami, S. Geometry of Ricci solitons admitting a new geometric vector field. AUT Journal of Mathematics and Computing, 2024; (): -. doi: 10.22060/ajmc.2024.23142.1234
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