Bakry-Emery Ricci curvature of Halilsoy metric

Abstract

The objective of this paper is to investigate Ricci curvature and its generalized notion of curvature on the Halilsoy spacetime. The Bakry--Émery Ricci tensor $Ric_f$ and $m-$Bakry--Émery Ricci tensor $Ric_f^m$ has been calculated with the potential function $f$. Aslo, the notion of Bakry--Émery scalar curvature $\mathcal R_f$ and $m-$Bakry--Émery scalar curvature $\mathcal R_f^m$ have been introduced, which is analogous to the scalar curvature, and such quantities have determined for Halilsoy spacetime. Finally, some sufficient conditions have been obtained for the flatness with respect to the curvatures $\mathcal R_f$ and $\mathcal R_f$.